## and its Relations to Modern Analysis and Algebra

was held in August 19–25, 2001 in Prague, Czech Republic. It was organized by the Mathematical Institute of the Czech Academy of Sciences and the International Mathematical Union in cooperation with the Department of Mathematics of the Institute of Chemical Technology, the Department of Mathematics of the University of Economics, and the Faculty of Mathematics and Physics of the Charles University.

### Organizing committee

• S. Donaldson (representative of IMU)
• M. Hušek (chairman)
• B. Balcar (vicechairman)
• P. Simon (secretary)
• R. Roháčková (treasurer)
• J. Coufal
• P. Holický
• O. Kalenda
• A. Klíč
• J. Pelant
• V. Trnková

TOPOSYM was sponsored by the International Mathematical Union, by the grants of organizers, by Czech Airlines, Elsevier and Conforg.

The Symposium was attended by 209 mathematicians from 35 countries. The scientific programme 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 the Topology Atlas.

### List of countries

The table summarizes the number of participants from individual countries.

 USA 26 Poland 23 Czech Republic, Mexico 19 Italy 12 United Kingdom 10 Russia 9 Canada 9 Israel, Japan 8 Germany, the Netherlands, Spain 7 Hungary 6 New Zealand 5 Slovenia 4 France, Greece, Portugal, South Africa 3 Egypt, Latvia, Slovakia 2 Belgium, Bulgaria, Denmark, Finland, Iran, Ireland, Lebanon, Malta, Oman, Sweden, Turkey, Yugoslavia 1

### List of presentations

The invited talks are in boldface.

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

### Photos

The pictures come mostly from scientific program of the conference The rest comes from various cultural and social events organized during the conference. Unfortunately, it was not possible to collect pictures of all the participants. The photographs were kindly offered by T. Hoshina, M. Hušek, E. Murtinová, P. Simon, J. Vaughan and Y. Yajima.