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.
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).
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 |
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. |
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).
TOPOSYM 2022