Topology Atlas Document # ppae-00


Proceedings of the Ninth Prague Topological Symposium

Contributed papers from the symposium held in Prague, August 19-25, 2001

Edited by Petr Simon

This collection of thirty two reviewed articles covers several fields of General Topology. Several contributions represent invited presentations at the Ninth Prague Topological Symposium.


Publication data
Ninth Prague Topological Symposium
Existence of a sublinear continuous order-preserving function for a noncomplete preorder on a topological vector space
Gianni Bosi and Magalí E. Zuanon
pp. 1-8
Some equivalences for Martin's Axiom in asymmetric topology
Bruce S. Burdick
pp. 9-13
The maximal G-compactifications of G-spaces with special actions
V. A. Chatyrko and K. L. Kozlov
pp. 15-21
Concerning the dual group of a dense subgroup
W. W. Comfort, S. U. Raczkowski and F. Javier Trigos-Arrieta
pp. 23-35
van Douwen's problems related to the Bohr topology
Dikran Dikranjan
pp. 37-50
On Tychonoff-type hypertopologies
Georgi Dimov, Franco Obersnel and Gino Tironi
pp. 51-70
Chainable subcontinua
Edwin Duda
pp. 71-73
On finite T0 topological spaces
A. El-Fattah El-Atik, M. E. Abd El-Monsef and E. I. Lashin
pp. 75-90
Transfinite sequences of continuous and Baire 1 functions on separable metric spaces
Márton Elekes
pp. 91-92
Characterizing continuity by preserving compactness and connectedness
János Gerlits, István Juhász, Lajos Soukup and Zoltán Szentmiklóssy
pp. 93-118
The Cantor set of linear orders on N is the universal minimal S\infty-system
Eli Glasner
pp. 119-123
On the metrizability of spaces with a sharp base
Chris Good, Robin W. Knight and Abdul M. Mohamad
pp. 125-134
Sub-representation of posets
M. K. Gormley and T. B. M. McMaster
pp. 135-146
Fell-continuous selections and topologically well-orderable spaces II
Valentin Gutev
pp. 147-153
Special metrics
Yasunao Hattori
pp. 155-164
Compactification of a map which is mapped to itself
A. Iwanik, L. Janos and F. A. Smith
pp. 165-169
Sequence of dualizations of topological spaces is finite
Martin Maria Kovár
pp. 171-179
On Lebesgue Theorem for multivalued functions of two variables
Grazyna Kwiecinska
pp. 181-189
A survey of J-spaces
E. Michael
pp. 191-193
Using nets in Dedekind, monotone, or Scott incomplete ordered fields and definability issues
Mojtaba Moniri and Jafar S. Eivazloo
pp. 195-203
Proper and admissible topologies in the setting of closure spaces
Mila Mrsevic
pp. 205-216
An intrinsic characterization of p-symmetric Heegaard splittings
Michele Mulazzani
pp. 217-222
Morita equivalence in the context of Hilbert modules
Jan Paseka
pp. 223-251
Orbits of turning points for maps of finite graphs and inverse limit spaces
Brian Raines
pp. 253-263
Wallman-Frink proximities
Marlon C. Rayburn
pp. 265-270
Fuzzy functions and an extension of the category L-Top of Chang-Goguen L-topological spaces
Alexander P. Sostak
pp. 271-294
Pushout stability of embeddings, injectivity and categories of algebras
Lurdes Sousa
pp. 295-308
On lower semicontinuous multifunctions in quasi-uniform and vector spaces
Andrzej Spakowski
pp. 309-319
Quasiorders on topological categories
Vera Trnková
pp. 321-330
Compactifications of topological groups
Vladimir Uspenskij
pp. 331-346
A locally connected continuum without convergent sequences
Jan van Mill
pp. 347-352
Nonstandard proofs of Eggleston like theorems
Szymon Zeberski
pp. 353-357

Publication data

Copyright © 2002 by Topology Atlas and Charles University. All rights reserved. Unless noted otherwise, authors retain copyright for their work. The articles in this volume may only be republished with permission of the copyright holders, except for brief excerpts in reviews and scholarly analysis. Metadata for original articles and reference lists is available from the publisher.

Proceedings of the Ninth Prague Topological Symposium.
Contributed papers from the symposium held in Prague, August 19-25, 2001.
Edited by Petr Simon.
Includes bibliographic references. xvii + 357 pages
ISBN 0-9730867-0-X

Mathematics Subject Classification (2000): 54-06

Published April 2002 by Topology Atlas
Toronto, Ontario, Canada


All contributions to this volume have been refereed anonymously.

Unless noted otherwise, authors retain copyright for their works.

Unless noted otherwise, all articles are in final form and the authors have not indicated that the articles will be submitted for publication elsewhere.

Copyright for the proceedings volume as a collection is held by Topology Atlas and the Prague Toposym organizing committee (Charles University).

Thanks to World Scientific Publishing Co. for permission to reprint material from Journal of Knot Theory and its Ramifications.

Thanks to Elsevier Science B.V. for permission to reprint material from Topology and its Applications and Theoretical Computer Science.


This collection is stored in the Mathematics arXiv (math.GN/0204165) and the Electronic Library of Mathematics.

Gzipped tar archive of LaTeX source files: toposym_tex.tar.gz (444 KB).

Ninth Prague Topological Symposium

The Ninth Prague Topological Symposium, International Conference on General Topology and its Relations to Modern Analysis and Algebra, August 19-25, 2001, was organized under the auspices of:

in cooperation with:

The organizers:

Toposym was partly sponsored by International Mathematical Union, by grants of organizers, by Czech Airlines, by Elsevier and by Conforg (A. Kotesovcová).

The Symposium was attended by 209 mathematicians from 35 countries.

The scientific program consisted of 41 lectures invited by the organizing committee, 103 oral contributions presented in four parallel sections, 14 posters and 9 enlarged abstracts.

Many contributions together with abstracts are published at Topology Atlas.

The conference took place on the campuses of the University of Economics (scientific program) and of the Prague Institute of Chemical Technology (accommodation and meals) in the southern part of Prague.

During the conference, several social and cultural events were organized: welcome and farewell rauts, a sightseeing tour in Prague, an organ concert in a church, guided tours in Prague for accompanying persons, and a whole day tour to a crystal glass factory at Nizbor, a classicist castle Kozel near Pilsen with a dinner in a country farm restaurant.


Countries in brackets were selected from addresses given by participants. Some names of countries are given in their shorter non-official form.

Abd El-Fattah El-Atik (Egypt)
Mohamed Ezzat Abd El Monsef (Egypt)
Gerardo Acosta (Mexico)
Sergei Ageev (Canada)
Gloria Guadalupe Andablo Reyes (Mexico)
Alexander Vladimirovich Arhangel'skii (Russia, USA)
Bohuslav Balcar (Czech Republic)
Zoltán T. Balogh (USA)
Artur Barkhudaryan (Czech Republic)
Barbora Batíková (Czech Republic)
Murray Bell (Canada)
Aleksander Blaszczyk (Poland)
Gianni Bosi (Italy)
Ahmed Bouziad (France)
David Buhagiar (Malta)
Lev Bukovský (Slovakia)
Inese Bula (Latvia)
Bruce Burdick (USA)
Dennis Burke (USA)
Eva Butkovicová (United Kingdom)
Alexander Bykov (Mexico)
Francesca Cagliari (Italy)
Jiling Cao (Japan)
Félix Capulín (Mexico)
Bernardo Cascales (Spain)
Matija Cencelj (Slovenia)
Jozef Chaber (Poland)
Michael Charalambous (Greece)
Janusz Jerzy Charatonik (Mexico)
Vitalij Chatyrko (Sweden)
Krzysztof Ciesielski (Poland)
Wistar Comfort (USA)
Agustin Contreras-Carreto (Mexico)
Eva Coplakova (the Netherlands)
Camillo Costantini (Italy)
Ákos Császár (Hungary)
José Antonio Cuenca Mira (Spain)
Brian van Dam (New Zealand)
Elias David (United Kingdom)
Edgar Diaz (Mexico)
Debora Di Caprio (Canada)
Jan Dijkstra (The Netherlands)
Dikran Dikranjan (Italy)
Giuseppe Di Maio (Italy)
Edwin Duda (USA)
Marton Elekes (Hungary)
H. Nurettin Ergun (Turkey)
Ilijas Farah (USA)
David Heaver Fremlin (United Kingdom)
Paul Gartside (USA)
David Gauld (New Zealand)
Stefan Geschke (Germany)
Eli Glasner (Israel)
Aneirin Glyn (United Kingdom)
Gilles Godefroy (France)
Chris Good (United Kingdom)
Rafal Gorak (Poland)
Isaac Gorelic (Canada)
Michael Kieran Gormley (United Kingdom)
Sina Greenwood (New Zealand)
Valentin Gregori (Spain)
Joachim Grispolakis (Greece)
Gary Gruenhage (USA)
Theo Grundhöfer (Germany)
Alexandra S. Gul'ko (Russia)
Riccardo Gusso (Italy)
Valentin Gutev (South Africa)
Goncalo Gutierres (Portugal)
Israel Gutik (Israel)
Klaas Pieter Hart (the Netherlands)
Yasunao Hattori (Japan)
Robert Heath (USA)
Melvin Henriksen (USA)
David Herrera (Mexico)
Neil Hindman (USA)
Ulrich Höhle (Germany)
Dirk Hofmann (Portugal)
Lubica Holá (Slovakia)
Petr Holický (Czech Republic)
Takao Hoshina (Japan)
Michael Hrusák (the Netherlands)
Miroslav Husek (Czech Republic)
Stavros Iliadis (Greece)
Alejandro Illanes (Mexico)
Gerald Itzkowitz (USA)
Saeid Jafari (Denmark)
István Juhász (Hungary)
Heikki Jaakko Kalervo Junnila (Finland)
Ondrej Kalenda (Czech Republic)
Jan Kolár (Czech Republic)
Anatoly Kombarov (Russia)
Andrzej Komisarski (Poland)
Martin Kovár (Czech Republic)
Konstantin Leonidovich Kozlov (Russia)
Jan Kraszewski (Poland)
Adam Krawczyk (Poland)
David Kruml (Czech Republic)
Pawel Krupski (Poland)
Iwona Krzeminnska (Poland)
Jerzy Krzempek (Poland)
Wieslaw Kubis (Israel)
Andrzej Kucharski (Poland)
John Kulesza (USA)
Kenneth Kunen (USA)
Hans-Peter Künzi (South Africa)
Grazyna Kwiecinska (Poland)
Arkady Leiderman (Israel)
Zbigniew Lipecki (Poland)
Victoria Lubitch (Israel)
David Lutzer (USA)
Michal Machura (Poland)
Sergio Macías (Mexico)
Fernando Macias-Romero (Mexico)
Endre Makai (Hungary)
Joze Malesic (Slovenia)
Witold Marciszewski (Poland)
Andrew Marsh (USA)
Verónica Martínez de la Vega (Mexico)
Phethiwe Precious Matutu-Mabizela (South Africa)
Ron McCartney (United Kingdom)
Aisling McCluskey (Ireland)
Dave McIntyre (New Zealand)
Enrico Meccariello (Italy)
Michael Megrelishvili (Israel)
Ernest Michael (USA)
Henryk Michalewski (Poland)
Chiara Milan (Italy)
Pawel Milewski (Poland)
Jan van Mill (The Netherlands)
Abdul-Adheem Mohamad (Oman)
Mojtaba Moniri (Iran)
Kazuhiko Morishita (Japan)
Neza Mramor Kosta (Slovenia)
Mila Mrsevic (Yugoslavia)
Michele Mulazzani (Italy)
Eva Murtinová (Czech Republic)
Arafa Nasef (Egypt)
Jacek Nikiel (Lebanon)
Juana Nunez Garcia (Spain)
Peter Nyikos (USA)
Franco Obersnel (Italy)
Fernando Orozco (Mexico)
Carlos Paniagua (Mexico)
Jan Paseka (Czech Republic)
Boris Alekseevich Pasynkov (Russia)
Jan Pelant (Czech Republic)
Patricia Pellicer Covarrubias (Mexico)
Vladimir Pestov (New Zealand)
Roberto Pichardo Mendoza (Mexico)
Zbigniew Piotrowski (USA)
Pavel Podbrdský (Czech Republic)
Elzbieta Pol (Poland)
Gerhard Preuß (Germany)
Pavel Pyrih (Czech Republic)
Brian Raines (United Kingdom)
Marlon C. Rayburn (Canada)
Mike Reed (United Kingdom)
Miroslawa Renska (Poland)
Dusan Repovs (Slovenia)
Günther Richter (Germany)
Masami Sakai (Japan)
Enrique A. Sánchez Pérez (Spain)
Antonio Sánchez Sánchez (Spain)
Almanzor Sapena (Spain)
Arjen Sevenster (the Netherlands)
Dmitri Shakhmatov (Japan)
Leonid Shapiro (Russia)
Ivailo Atanasov Shishkov (Bulgaria)
Petr Simon (Czech Republic)
Olga Sipacheva (Russia)
Josef Slapal (Czech Republic)
Nancy L. Smith (USA)
Frank A. Smith (USA)
Slawomir Solecki (USA)
Alexander Sostak (Latvia)
Lajos Soukup (Hungary)
Lurdes Sousa (Portugal)
Andrzej Spakowski (Poland)
Berd van der Steeg (the Netherlands)
Dona Strauss (United Kingdom)
Zoltán Szentmiklóssy (Hungary)
Egbert Thümmel (Czech Republic)
Mikhail Tkachenko (Mexico)
Vladimir Tkachuk (Mexico)
Stevo Todorcevic (France)
Vera Trnková (Czech Republic)
H. Murat Tuncali (Canada)
Marian Turzanski (Poland)
Edward D. Tymchatyn (Canada)
Piotr Urbaniec (Poland)
Vladimir Uspenskij (USA)
Vesko Valov (Canada)
Jerry Vaughan (USA)
Fernando Velazquez-Castillo (Mexico)
Paolo Vitolo (Italy)
Stephen Watson (Canada)
Martin Weese (Germany)
Scott Williams (USA)
Bart Windels (Belgium)
regory Wisloski (USA)
Yukinobu Yajima (Japan)
Andrei Yakivchik (Russia)
Kaori Yamazaki (Japan)
Ivan Yaschenko (Russia)
Szymon Zeberski (Poland)
Miroslav Zelený (Czech Republic)
Grigori Zhitomirski (Israel)
Ondrej Zindulka (Czech Republic)
Magalì E. Zuanon (Italy)


Invited talks are in bold face.

El-Atik Abd El-Fattah, Approximation of fractals by finite topological spaces (poster)
El Monsef M. E. Abd, On the behavior of pre-generalized closed sets and their generalizations Acosta G., Problems on continua having unique hyperspace
Ageev S., Topology of the Nöbeling spaces
Andablo Reyes G. G., Ordered embeddings on symmetric products
Arhangel'ski, A. V., Topological spaces with some algebraic structure
Balogh Z., Reflection theorems and elementary submodels
Barkhudaryan A. Clones of topological spaces
Bell M., Polyadic spaces of countable tightness
Blaszczyk A., Extension of Vladimirov's theorem
Bosi G. and Zuanon M. E., Existence of a sublinear continuous order-preserving function for a noncomplete preorder on a topological vector space
Bouziad A., H-trivial spaces
Bula I., On strict convexity in metric spaces (poster)
Burdick B., On linear cofinal completeness
Burke D., First countable, countably paracompact spaces
Bykov A., On SSDR pro-maps
Cagliari F., Injective topological fibre spaces (poster)
Cao J., Cardinal Invariants of star-covering Properties
Capulín F., Retractions from C(X) onto X and type N-continua
Cascales B., The Lindelöf property in Banach spaces
Cencelj M. Extension of maps to nilpotent spaces
Chaber J. Hereditarily Baire spaces
Charatonik J.J., On self-homeomorphic dendrites
Chatyrko V., On a question of de Groot and Nishiura
Ciesielski K., A generalization of Sperner's lemma
Comfort W. W., The dual group of a dense subgroup
Contreras-Carreto A., Compactness properties of spaces Cp(X,2) and Cp(X,Z)
Costantini C., Consistent examples about extensions of continuous functions
Császár Á., Rarophile spaces (poster)
van Dam B., The construction method of resolutions
David E., Ideals of quasi-ordered sets
Dijkstra J., On the structure of n-point sets
Dikranjan D., The Bohr topology can measure Boolean subgroups
Di Maio G., Uniformizable and metrizable Delta-U proximal topologies (poster)
Duda E., Chainable subcontinua (enlarged abstract)
Elekés M., Linearly ordered sets of continuous and Baire 1 functions
Ergun H.N., On weak \overline\theta-refinability
Farah I., Powers of Cech-Stone compactifications
Fremlin D. H., Topological measure spaces
Gartside P., Relative properties
Geschke S., Cardinal invariants of the continuum related to convex geometry
Glasner E., Universal minimal dynamical systems
Godefroy G., Some recent progress in the topology of Banach spaces
Good C., Whether monotonically countably paracompact spaces are collectionwise Hausdorff depends on whether you have one or two measurable cardinals
Gorak R., Spaces u-equivalent to the n-disk
Gorelic I., Partial orders with singular cofinalities
Gormley M. K., The embeddability ordering and order-resolutions (poster)
Greenwood S., Ideal reflections
Gregori V., On completion of fuzzy metric spaces
Grispolakis J., On the existence of periodic cycles on the boundary of a Siegel disc (enlarged abstract)
Gruenhage G., Recent developments in generalized metric spaces
Gul'ko A.S., Free rectifiable spaces
Gusso R., Large and small sets with respect to homomorphisms and products of groups (enlarged abstract)
Gutev V., Subdividing and generating embedding-like properties
Gutierres G., Is R a sequential space?
Hart K. P., Algebraic and logical aspects of hereditary indecomposability
Hattori Y., Special metrics
Heath R., Continuity of addition on some ccc liniarly ordered spaces and related spaces
Henriksen M., Spaces X in which all prime z-ideal of C(X) are minimal or maximal
Herrera D., Hyperspaces of dendrites
Hindman N., Recent progress in the theory of topological semigroups and the algebra of \beta S
Höhle U., A remark on the hypergraph functor
Hofmann D., Lax algebras
Holá L., Spaces of densely continuous forms, usco and minimal usco maps
Holický P., On the sets with small sections over nonseparable spaces
Hrusák M., How much \diamondsuit does your construction require?
Iliadis S., A dimension-like function of type Ind
Illanes A., Size levels
Itzkowitz G., Balance, functional balance, and discrete balance In topological groups
Jafari S., \theta-c-semiopen sets and associated mappings (enlarged abstract)
Juhász I., Characterizing continuity by preserving compactness and connectedness
Junnila H. J. K., On function spaces
Kalenda O., On the class of continuous images of Valdivia compacta
Kombarov A., Normality-type properties and functors (enlarged abstract)
Komisarski A., Descriptive set-theoretic properties of the isomorphism relation between Banach spaces
Kovár M., Problem 540 is (almost) solved
Kozlov K. L., The maximal G-compactifications as completions
Kraszewski J., Properties of ideals on the generalized Cantor spaces
Krawczyk A., Ordering of itineraries
Kruml D., On simple and semisimple quantales
Krupski P., Continuous means on solenoids
Krzeminska I., Uniform continuum-chainability and Whitney levels
Krzempek J., An approach to covering dimension of maps
Kubis W., On cardinalities of cliques in Borel non-convex sets
Kunen K., Ultrafilters and Matrices
Künzi H.-P., Quasi-uniformities on topological semigroups and bicompletion
Kwiecinska G., On Lebesgue theorem for multivalued functions of two variables (poster)
Leiderman A., On the spaces of Lipschitz functions
Lipecki Z., Linearly independent perfect sets of large cardinality
Lubitch V., A linearly Lindelöf non-Lindelöf space from a good PCF scale
Lutzer D., Recent progress in ordered spaces
Machura M., Continuous functions coupling with almost contained
Macías S., Arcwise accessibility in hyperspaces
Macías-Romero F., On span and other classes of continua
Makai E., Characterization of function classes C(Y)|X
Malesic J., Self similar Cantor sets in Euclidean spaces
Marciszewski W., Some recent results on the function spaces Cp(X)
Marsh A., Symmetries of wild knots
Martínez de la Vega V., An uncountable collection of compactifications of the ray with remainder pseudo-arc.
Matutu-Mabizela P.P., Stably continuous sigma frames (poster)
McCluskey A., Relative normality within the Sorgenfrey plane
McIntyre D., Topology Dictionary and Topology Encyclopædia (poster)
Meccariello E., Graph topologies on closed multifunctions, I (poster)
Megrelishvili M., Fragmentability and representations of flows
Michael E., A Survey of J-spaces
Michalewski H., Condensations of function spaces onto compacta
Milan C., Continuous dualities of locally compact modules (enlarged abstract)
Milewski P., On typical parametrizations of n-dimensional compacta on the Cantor set
van Mill J., Another proof of the Open Mapping Principle and applications
Mohamad A.-A., Metrization and sharpe bases
Moniri M., Using nets in Dedekind, monotone, or Scott incomplete ordered fields and definability issues
Morishita K., On Eberlein compactifications of metrizable spaces
Mramor Kosta N., Actions of tori on CW complexes
Mrsevic M., Function spaces in Cech closure spaces
Mulazzani M., An intrinsic characterization of p-symmetric Heegaard splittings
Murtinová E., Separation axioms in dense subsets
Nasef A., On upper and lower \gamma-irresolute multifunctions
Nikiel J., On \sigma-directed inverse systems
Nunez García J., Strongly nuclear groups
Nyikos P., New axioms and techniques in set-theoretic topology
Obersnel F., On Tychonoff-type hypertopologies
Orozco F., Increasing Whithey properties
Paseka J., Morita equivalence for non-commutative topologies
Pasynkov B.A., On homogeneous and Dugundji compacta X with dim X < ind X
Pelant J., On selections and continuous functions
Pellicer Covarrubias P., On properties of the hyperspaces K(X)
Pestov V., Spaces with metric and measure, topological transformation groups, and Ramsey theory
Piotrowski Z., A solution of a problem of Henriksen and Woods on separate vs. joint continuity
Pol E., On hereditarily indecomposable continua, Henderson compacta and a question of Yohe
Preuß G., A better framework for first countable spaces
Pyrih P., Open problem seminar (poster)
Raines B., Orbits of turning points for maps of finite graphs and inverse limit spaces
Rayburn M.C., Wallman-Frink proximities (poster)
Reed M., Developments in topology and domain theory
Renska M., On rigid hereditarily indecomposable continua
Repovs D., A survey of geometric topology of polyhedra
Richter G., Exponentiablity for maps means fiberwise core-compactness (enlarged abstract)
Sakai M., Orderability of free topological groups,
Sánchez Pérez E.A., Weak topologies on asymmetric normed linear spaces
Sapena A., Uniform continuity in fuzzy metric spaces
Shakhmatov D., Convergence properties of topological groups
Shapiro L., Dyadic compacta
Shishkov I.A., Selections of mappings with collectionwise normal and continuum-paracompact domain
Sipacheva O., Topological solvability of equations over groups
Slapal J., A digital analogy of the Jordan curve theorem (enlarged abstract)
Smith F.A., Compactification of a set mapped into itself (poster)
Solecki S., Borel equivalence relations and topology
Sostak A., On some L-valued categories related to topology
Soukup L., Cardinal sequences of scattered spaces
Sousa L., Pushout stability of embeddings, injectivity and categories of algebras
Spakowski A., On lower semicontinuous multifunctions in quasi-uniform spaces (enlarged abstract)
van der Steeg B., Model-theoretic continuum theory
Strauss D., Multiplication in WAP(N) and SAP(N)
Tkachenko M., R-factorizable groups and P-groups
Tkachuk V., Lindelöf \Sigma-spaces and Cp-theory: recent achievements
Todorcevic S., Chain-condition methods in topology
Trnková V., Quasiorders on topological categories
Tuncali H.M., On dimensionally restricted maps
Turzanski M., A combinatorial lemma for a symmetric triangulation of the sphere S2
Urbaniec P., Topological games and iterates of multifunctions
Uspenskij V., Compactifications of topological groups
Valov V., Dense families of selections and finite-dimensional spaces
Vaughan J., Examples of linearly stratifiable spaces
Watson S., Applying trees of finite approximations of elementary submodels to topology
Williams S., Topologies on infinite products
Windels B., Quantifying domains
Yajima Y., Covering properties and various products
Yakivchik A., Around Katetov theorems on products
Yamazaki K., Weak C-embedding and products with a compact factor
Yaschenko I., On spaces with topology determined by almost closed sets
Zeberski S., Nonstandard proofs of Eggelston like theorems
Zhitomirski G., Topologically complete representations of inverse semigroups
Zindulka O., Small opaque sets (poster)

Copyright © 2002 Charles University and Topology Atlas. Published April 2002.