## and its Relations to Modern Analysis and Algebra

was held on August 24–28, 1981 in Prague, Czech Republic. It was organized by the Institute of Mathematics of the Czechoslovak Academy of Sciences with support from the International Mathematical Union in cooperation with the Faculty of Mathematics and Physics of the Charles University, the Institute of Mathematics of the Slovak Academy of Sciences, the Faculty of Mathematics and Physics of the Comenius University and the Association of Czechoslovak Mathematicians and Physicists.

Support for the Symposium was also provided by the Faculty of Electrical Engineering and the Faculty of Nuclear and Physical Engineering of the Czech Technical University, the Faculty of Natural Sciences of the Purkyně University and the Faculty of Natural Sciences of the Palacký University.

### Organizing committee

• J. Novák (chairman)
• Z. Frolík (vice-chairman)
• S. Schwarz (vice-chairman)
• V. Koutník (secretary)
• A. Rážek (treasurer)
• B. Balcar
• L. Bukovský
• J. Hejcman
• M. Hušek
• M. Katětov
• T. Katrinák
• I. Kolár
• J. Kolomý
• L. Mišík
• J. Pelant
• P. Pták
• V. Pták
• A. Pultr
• J. Reiterman
• J. Rosický
• I. Sekanina
• P. Simon
• V. Trnková
• J. Vilímovský
• P. Vrbová

The Symposium was attended by 227 mathematicians from 27 countries, including 61 from Czechoslovakia. The scientific program was prepared by the Program Committee consisting of Z. Frolík (chairman), M. Katětov (vice-chairman) and M. Hušek. The program consisted of 34 lectures invited by the organizing committee and 133 contributed papers presented in four parallel sessions.

On Monday afternoon a special session devoted to the commemoration of the 200th anniversary of the birth of Bernard Bolzano was held at Charles University. On that occasion, the Presidium of Czechoslovak Academy of Sciences awarded a Golden Plaque of B. Bolzano for merit in mathematical sciences to P. S. Alexandrov, R. D. Anderson and Á. Császár.

96 invited and contributed papers were published in General Topology and its Relations to Modern Analysis and Algebra V, Proceedings of the Fifth Prague Topological Symposium 1981 (Heldermann Verlag 1983).

### List of countries

The table summarizes the number of participants from individual countries.

 Czechoslovakia 60 Poland 33 USSR 21 Germany (East 5, West 14) 19 USA 16 Yugoslavia 12 Italy, the Netherlands 9 Hungary 8 Belgium, Bulgaria, Canada 5 Greece 4 Egypt, United Kingdom 3 Austria, Finland, India, Spain 2 Denmark, France, Ireland, Japan, Kuwait, Mexico, Venezuela 1

### List of communications

The invited lectures are in boldface.

 Abd El-Monsef, El-Deeb, Hasanein, Miashhour On non-continuous mappings. Abd El-Monsef, Ghanim, Kerre, Mashhour Fuzzy topological results. Abel The extensions of topological spaces depending on cover and its applications. Adámek, Reiterman Cartesian closed hull of uniform spaces. Amirdžanov On dense subspaces of topological spaces. Anderson Infinite dimensional topology Argyros, Mercourakis, Negrepontis Analytic properties of Corson-compact spaces. Arhangelskii On relationships between topological properties of $X$ and $C_p(X)$. Arya Sum theorems for topological spaces I. Baković On Hurewicz families of separable metric spaces. Balogh On hereditarily strong $\sum$-spaces. Balcar, Simon Cardinal invariants in Boolean spaces. Banaschewski The power of the ultrafilter theorem. Bell Compactifications of a countable discrete space. Błaszczyk A note on rigid spaces and rigid Boolean algebras. Borubaev On the completion of finite order of uniform spaces. Brandenburg On D-normal spaces. Bregman, Šapirovskij On partition of topological spaces. Bula A short proof that a compact ordered space cannot be mapped onto a non-metric product. Butkovičová Gaps in Rudin-Frolík order. Čerin Global convergences of compacta. Chaber Open finite-to-one images of metric spaces. Charatonik Several problems on universal smooth dendroids. Charatonik, Miklos Images of graphs under local expansions. Chvalina On continuous functional parametrizations of topological general systems. Čoban Algebras and some questions of the theory of maps. Collins A one line proof of the fact that the topology of compact convergence of continuous functions is the compact-open topology. Contessa, Zanolin On some remarks about a not completable convergence ring. Császár Á. Complete extensions of quasi-uniform spaces. Császár K. Absolutely open spaces. Czuba Open functions and pointwise smooth dendroids. Daneš A covering theorem for mappings between metric spaces. Demaria On regular functions from a topological space to a graph. Dikranjan Extension of minimal ring topologies. Dimov On the Stone duality. Dobrakov Uniform boundedness principle for exhaustive set functions. Dobrowolski An extension of a theorem of Klee. Doitchinov Supertopologies and some classes of extensions of topological spaces. van Douwen Continua and $\beta X$. Dow Remote points. Duchoň Harmonic analysis of vector functions and measures on homogenous Banach spaces. Duda A sum theorem for semispan of continua. Engelking, Pol E. Countable-dimensional spaces: a survey. Fabian, Withfield, Zizler On smooth characterizations of spaces isomorphic to Hilbert or uniformly convex spaces. Fedorchuk Absolute retracts and some functors. Felouzis On the characterization of totally orderable spaces and their subspaces. Ferry Homotopy, simple homotopy and compacta. Flachsmeyer On the convergence of motions. Fremlin Consequences of Martin's axiom. Frič, Kent A nice completion need not be strict. Frič, Koutník Sequential convergence since Kanpur conference. Frolík, Hušek, Pelant, Rödl, Vilímovský Uniform spaces (selected topics). Gähler S. Topological problems in optimization theory. Gähler W. A topological approach to general structure theory. García-Máynez Chromatic numbers and Cantor manifolds. Giuli, Strecker, Tozzi On E-dense hulls and shape theory. Graf Realizing homomorphisms of category algebras. Grimeisen Remarks on the continuity of incidence relations in topological planes. Guido A characterization of simple extensions of topologies. Hadžiivanov O stěpeni svjaznosti proizveděnij topologičeskich prostranstv. Hajnal, Szentmiklóssy On the cardinality of quasi hereditarily Lindelöf spaces. Hansell Point-countable Souslin-additive families and $\sigma$-discrete reduction. Hart Topological properties of $\omega_1$-trees. Hejcman Metrization lemmas and equivalence of Lipschitz structures. Henriksen, Smith Sums of z-ideals and semiprime ideals. Herrlich Categorical topology 1971-1981 Himshiashvili On the Euler characteristics of the level surfaces of smooth germs. Hohti A theorem on uniform paracompactness. Hušek Omitting cardinal functions by topological spaces. Hušek, Reichel On linearly uniformizable spaces. Iliadis Regular spaces (in the sense of the theory of order). Ivanšić A note on Borsuk's index e(X). Janković Properties of $\alpha\beta$-continuous functions. Jayne First level Borel functions. Jelić Aksiomy $PSR_i$ v bitopologičeskich prostranstvach. Juhász Quasi hereditary Lindelöfness and the S space problem. Junnila On stratifiable spaces and $M_0$-spaces. Kamiński Remarks on multivalued convergences. Kaniewski, Rogers Double uniformization. Kartsaklis An attempt of unification of mikrocosmos and mega(makro)-cosmos on the base of the order. Katětov On a dimension function based on Bolzano's ideas. Katrnoška M-base and the representation of orthocomplemented posets. Kolář Functorial prolongations of Lie groups and their actions. Kolomý Duality mapping and geometry of Banach spaces. Kovačević Continuity and paracompactness. Kratochvíl Sequential convergence as a partial operation. Krupski A characterization of solenoids Kurepa Some approaches to topological spaces. Laitadze On iterated products of models with topologies. Laugwitz On Bolzano's nonarchimedean numbers. Lecomte Automorphisms of a vector bundle. Levi On Baire cosmic spaces. Levy, Rice The approximation and extension of uniformly continuous mappings. Lisica Duality theorems and shape and coshape dual categories. Lokucievskij On topology of continua. Lowen Hyperspaces of fuzzy sets. Lowen-Colebunders On two uniformization problems for Cauchy spaces. Makai The full embeddings of the category of proximity spaces into itself. Maltsev Iterative algebras of continuous functions. Mamuzić A note on an elementary phenomenon in general topology. Marjanović Identification of some hyperspace constructions. Martín-Peinador Irreducible maps and ultraspaces. Melton Hereditary factorization structures on $Top$ and $T_0$. van Mill Types of weak P-points in $\beta\omega\setminus\omega$ Miškin Upper and lower semicontinuous set-valued mappings of topological spaces. Močkoř Nonstandard topological completions. Mogilski On infinite dimensional sigma-compact manifolds. Mršević On non-symmetric proximity spaces. Musielak On filtered families of operators in two-modular spaces. Nagata Topics in dimension theory. Nedev Faktorizacija dokazatel'stv nekotorych teorem o selekcijach mnogoznačnych otobraženij. Nepomnjaščii A spectral characterization of absolute multivalued retracts. Nguyen-To-Nhu Remarks on characterizations of dimension of separable metrizable spaces. Neubrunn Multifunctions and quasicontinuity. Nyikos Set-theoretic topology of manifolds. Okuyama Some relationship between function spaces and hyperspaces by compact sets. Olejček An example of a recurrent function on a compact totally disconnected space. Pap Contributions to functional analysis on convergence spaces. Pareek On semi-metric spaces. Pietsch The index-trace formula for Fredholm operators. Pol E. Remarks on infinite-dimensional spaces. Pol R. On analytic-measurable collections of countable-dimensional and weakly infinite-dimensional compacta. Polkowski Open and closed mappings and infinite dimension. Poppe, Stärk Compactness of almost periodic functions and Bohr compactification. Porst Adjoint diagonals for topological completions. Preiss Dimension, metrics and differentiation of measures. Pták P. Topological quantum mechanical observables. Purisch Recent results on total orderability. Riečan On regular measures in ordered spaces. Roelcke Completeness of quotients of topological groups. Rosický Model theoretic properties of categories of topological type. Schroder Stone-Weierstrass approximation: algebraic problems. Schröder Factorizations in general categories (Submonotone quotient, Superlight). Shapiro On regular averagings. Ščepin On compacts defined by functors. Shaydayeva On basic concepts of non-commutative general topology. Singal Sum theorems for topological spaces II. Šipoš On semiconvergence semigroups. Šiška The LCC-topology on the space of continuous functions. Šostak Paracompacta with $G_\delta$-diagonal and inverse systems of ANRs. Swiatkowski, Wilczyński Remark on the theorem of Dini. Szymański, Zhou Hao-xua The behaviour of uu $\omega^{2*}$ under some consequences of Martin's axiom. Telgársky On a game of Choquet. Tholen Completions of categories and shape theory. Titoni Some remarks on radial and pseudoradial spaces. Tkačenko On topologies of free groups. Topsoe Topological games and Čech completness. Toruńczyk Hilbert manifolds in topological groups and in convex subsets of Banach spaces. Trnková Representations of comutative semigroups by products of topological spaces. Ungar Š. A remark on shape paths and homotopy pro-groups. Valov AR spaces in the class of completely regular spaces are compact spaces. Vaughan Embeddings of $(\omega_1, \omega_1^*)$-gap spaces in countably compact spaces. van de Vel Convex structures and dimension. Vinárek Homeomorphisms of products of metric 0-dimensional spaces. Vlach On nonenlarging closures in affine spaces. Vojtáš A transfinite Boolean game and a generalization of Kripke's embedding theorem. de Vries Glicksberg's theorem for G-spaces. Waszak On convergence in some two-modular spaces. Watson Countably paracompact first countable spaces. Wattel Partitions of ${\mathbb R}^n$ into $n+1$ homogeneous zero dimensional homeomorphic measurable parts. West Decomposition of Fredholm operators. Wilhelm Nearly lower semicontinuity and its applications. Williams Co-absolutes of Čech-Stone remainders and orderable spaces. Wong Homeomorphism spaces of Hilbert manifolds are ANR's. Zaharov Topological and algebraical aspects of some sets of measurable functions. Zambachidze On relations between dimensional and dimensional-like functions in some special classes of topological spaces and topological groups. Zemánek Asymptotic behaviour of some geometric characteristics of linear operators.

### Photos

There are two collections of pictures. The first one was made by an official photographer at the ceremony of awarding the Bolzano medals to R. D. Anderson, A. Csaszar and P. S. Alexanfroff (not present) in connection with TOPOSYM. Among those present one can see J. Nagata, A. V. Arhangelskii, M. Katětov, G. Grimeisen, F. B. Jones, R. Engelking, J. Aarts and L. de Groot.

The remaining pictures come from a private collection of M. Hušek and the photos were taken during a party taking place on a boat cruising the Vltava river. S. Eilenberg was a guest there (en route to another conference).