## and its Relations to Modern Analysis and Algebra

was held on August 23 27, 1976 in Prague, Czech Republic. It was organized by the Mathematical Institute of the Czechoslovak Academy of Sciences with support of the International Mathematical Union and in cooperation with the Slovak Academy of Sciences, the Faculty of Mathematics and Physics of the Charles University and the Association of Czechoslovak Mathematicians and Physicists.

### Organizing committee

• J. Novák (chairman)
• A. Rázek (treasurer)
• Z. Frolík
• J. Hejcman
• M. Hušek
• M. Katětov
• V. Koutník
• V. Pták
• S. Schwarz
• M. Sekanina
• V. Trnková

The Symposium was attended by 217 mathematicians from 24 countries, including 53 from Czechoslovakia. The program consisted of 30 invited talks (11 plenary, 18 semiplenary, 1 in a session for contributed papers), and 135 fifteen minute talks in three or four parallel sessions.

The proceedings of the symposium are published in parts A and B of General Topology and its Relations to Modern Analysis and Algebra IV, Proceedings of the Fourth Prague Topological Symposium 1976. Part A, published by Springer-Verlag, contains 19 invited papers. Part B, published by Association of Czechoslovak Mathematicians and Physicists, contains 98 contributed papers, 5 abstracts of invited talks and problems of K. Borsuk and of K. Morita.

### List of participants

 Aarts, Lowen-Colebunders On an example of Mary Ellen Rudin. Alexiewicz Two-norm algebras. Alster, Zenor Preservation of the Lindelöf property in product spaces. Anantharaman, Naimpally Equicontinuity, nonexpansiveness snd uniform boundedness Anderson Group actions on Hilbert cube manifolds. Arhangelskii Some recent results on cardinal-valued invariants of bicompact Hausdorff spaces. Arya On a theorem of Michael-Morita-Hanai. Atsuji On normality of the product of two spaces. Baayen Maximal linked systems in topology. Balogh Relative compactness and recent common generalizations of metric and locally compact spaces. Banaschewski Sheaves of Banach spaces. Bellamy Indecomposable continua with one and two composants. Bessaga, Dobrowolski Deleting formulas for topological vector spaces and groups Binz On an extension of Pontryagin's duality. Błaszczyk On a factorization lemma and a construction of absolute without separation axioms. Bogatyj On preservation of fixed point property by continuous mappings. Bognár On locally ordered spaces. Boseck, Czichowski Structure of connected locally compact groups. Byczkowski On closed graph and open mappings theorems. Čerin Homotopy theory at $\omega$ and the theory of shape. Chaber On $\theta$-refinability. Chapman Homotopy conditions which characterize simple homotopy equivalences. Charalambous A note on the dimension of products. Charatonik Problems and remarks on contractibility of curves. Chattopadhyay, Thron Extensions of closure spaces. Chvalina Set transformations with centralizers formed by closed deformations of quasi-discrete topological spaces. Čoban, Nedev Odno priloženie faktorizacionnych teorem dlja mnogoznačnych otobraženii. Comfort Some recent applications of ultrafilters to topology. Császár Á. Some problems concerning C(X). Császár K. Separation and connectedness. Dobrakov Products of operator valued measures and the Fubini theorem. Doitchinov The notion of K-shape. Domiaty Remarks to the problem of defining a topology by its homeomorphism group. van Douwen A technique for constructing examples. Durdil On the geometric characterization of differentiability. Dyckhoff Topology in a spatial topos. Efremovič, Vainštein Novye rezultaty v ravnomernoi topologii Fabian On singlevaluedness and continuity of monotone mappings. Flachsmeyer Topologization of Boolean algebras. Flachsmeyer, Terpe On convergence structures in the space of summations. Fleissner Box products of Baire spaces. Frič, Koutník Sequentially complete spaces. Frolík Recent development of theory of uniform spaces. Gähler On generalized topological vector spaces. Gähler On limit spaces and limit-uniform spaces. Gerlits On dyadic and $\lambda$-adic spaces. Gierz, Keimel A lemma on primes appearing in algebra and analysis. Govaerts Categories of continuous function apaces. Grimeisen The limit inferior of a filtered set-family as a set of limit points. Hadžiivanov O razmernosti metričeskich i kompaktnych prostranstv. Hajek Wallman extendible functions with normal domains. Hamburger A generalization of uniform open basis. Heinrich Linear-topological properties of operator spaces. Hejcman Covering dimensions and partitions of unity. Henriksen Spaces that haue a compactification with a countable remainder. Hilton On generalizations of shape theory. Holický On a characterization of completely additive families. Hoshina Compactifications by adding a countable number of points. Hušek, Trnková Categorial aspects are useful in topology. Iliadis O nepodvižnych točkach pri nekotorych otobraženijach kompaktov. Ivanov Fixed point theorems of metric space mappings. Ivanšić Embedding compacta up to shape. Iwanik On two-sided nonsingular transformations of Borel spaces. Jayne Analytic sets of extreme points of closed convex sets. Jeschek, Poppe, Stärk A compactness criterion for the space of almost periodic functions. Johnson Perturbations of Banach algebras. Juhász On the number of open sets. Kartsaklis Topological considerations in the foundations of quantum mechanics and space-time theories. Katětov Descriptive complexity of functions. Katuta Monotone increasing covers and paracompactness. Kaul Regularity: A generalization of equicontinuity. Keimel On structure spaces of vector lattices. Kent, Richardson Some product theorems for convergence spaces. Kneis The theorem of Arzela-Ascoli in pseudo-uniform spaces. Kratochvíl Multisequences and measure theory. Kulpa On decomposition into no where dense sets. Kuratowski $\sigma$-algebra generated by analytic sets and applications. Kurepa On monotone mappings of ordered sets. Kůrková Fine and simply fine uniform spaces. Kuzminov, Švedov O gomologičeskoi razmernosti Bredona nasledstvenno parakompaktnych prostranstv. Lokucievskij Axiomatic definition of the dimension for bicompacta. Lowen Convergence in the lattice of lower semicontinuous functions. Lüschow Some topological properties of SM-spaces. Maćkowiak Planable and smooth dendroids. Maharam-Stone Measure, category and Boolean spaces. Mardešić Recent development of shape theory. Marek Fredholm points of compactly perturbed bounded linear operators. Marjanović Some considerations related to hyperspaces. Meletiou Families of partially coinciding topologies. van Mill Recent results on superextensions. Minc Local connectedness and fixed points. Mioduszewski Compact Hausdorff spaces with two open sets. Mislove The maximal ideal space of the measure algebra of certain semigroups. Močkoř Topological groups of divisibility. Müller $T_3$ Musiał The weak Radon-Nikodym property in Banach spaces. Musielak An application of modular spaces to integral equations. Musielak, Waszak Some problems of convergence in countably modulared spaces. Mysior The category of all zero-dimensional realcompact spaces is not simple. Nagata On rings of continuous functions. Nagy On countably compact, locally countable spaces. Negrepontis Applications of Erdös-Rado intersection relations in the embedding of $l_1(\gama)$ to Banach spaces. Nel Subcategories with cartesian closed coreflective hulls. Nelson Algebras of continuous functions in universal algebra. Nešetřil, Rödl Some topological Ramsey-type problems. Neubrunn Separate continuity and continuity for some generalized continuity notions. Novák Concerning the Cartesian product of two Fréchet spaces. Nyikos Countable small rank and cardinal invariants. Pareek On dense subspaces of stratifiable and semi-stratifiable spaces. Patkowska A class $\alpha$ and compacta which are quasi-homeomorphic with surfaces. Patronis, Stavrinos On hyperspace of continuous curves and continuous hyperspaces of any order. Pelant Combinatorial properties of uniformities. Pelant, Reiterman Atoms in uniformities and proximities. Pietsch Entropy numbers of operators in Banach spaces. Pol E., Pol R. A hereditarily normal strongly zero-dimensional space containing subspaces of arbitrarily large dimension. Porst Embeddable spaces and duality. Preuss Relative connectedness and disconnectedness in topological categories. Prodanov Minimal topologies on Abelian groups. Pták P. Refinements of uniform spaces associated with discreteness. Pták V. Nondiscrete mathematical induction. Rajagopalan The V-process and a problem of Kannan and Arhangelskii on compact c-spaces. Reed Consistency and independence results in Moore spaces. Reichel Some results on distance-functions. Rice Descriptive sets in uniform spaces. Riečan Extension of measures and integrals by the help of a pseudometric. Ringrose Derivations of quotients of von Neumann algebras. Roitman Some topological effects of random and Cohen reals. Rosický Liftings of functors in topological situations. Rudin Set theoretic problems in topology. Ryškov O centrirovkach mnogomernych rešetok. Ščepin On uncountable inverse spectra. Schmets On spaces of vector-valued continuous functions. Schrijver Characterizations of supercompact spaces. Schröder Wallman's method (Das Wallman-Verfahren). Segal Local behavior in shape theory. Sekanina Topologies on $2^X$. Seyedin On quasi-uniform convergence. Simon Uniform atoms on $\omega$. Smirnov Some topological aspects in the theory of topological transformation groups. Šostak A class of spaces which contains all connected and compact spaces. Stone Measure-preserving maps. Švedov Ob ocenke metričeskoi razmernosti. Szökefalvi-Nagy Some properties of the function algebra $H^\infty$. Szymański P-points in $\beta\omega$. Talamo Extensions and structures. Tall Some topological applications of a generalized Martin's axiom. Tashjian Exponential operations in coreflective subcategories of Tych and Unif. Telgársky On some topological games. Vaughan Products of [a,b]-chain compact spaces. van de Vel The fixed point property of superextensions. Venkataraman On topological invariants of topological spaces. Vilímovský Extensions of uniformly continuous Banach ualued mappings. de Vries Embeddings of G-spaces. Wage On a problem of Katětov. Wattel Subbase structures in nearness spaces. Weiss Some connected problems. Wichterle Joint convergence in function spaces. Order of W-closures. Wicke, Worell Scattered spaces of point-countable type. Wilhelm On closed graph theorems. van Wouwe Generalized ordered p-spaces. Zahradník $l_1$-partitions of unity on normed spaces. Zarelua On zero-dimensional mappings and commutative algebra. Zaremba On cohesive mappings. Zemánek On the spectral radius in Banach algebras.