Zdeněk Frolík

Zdeněk Frolík (10 March 1933 – 3 May 1989) was a Czech mathematician. His research interests included topology and functional analysis. In particular, his work concerned covering properties of topological spaces, ultrafilters, homogeneity, measures, uniform spaces. He was one of the founders of modern descriptive theory of sets and spaces.

Two classes of topological spaces are given Frolík's name: the class P of all spaces such that is pseudocompact for every pseudocompact space , and the class C of all spaces such that is countably compact for every countably compact space .

Frolík prepared his Ph.D. thesis under the supervision of Miroslav Katetov and Eduard Čech.

Selected publications Generalizations of compact and Lindelöf spaces - Czechoslovak Math. J., 9 (1959), pp. 172–217 (in Russian, English summary) The topological product of countably compact spaces - Czechoslovak Math. J., 10 (1960), pp. 329–338 The topological product of two pseudocompact spaces - Czechoslovak Math. J., 10 (1960), pp. 339–349 Generalizations of the Gδ-property of complete metric spaces - Czechoslovak Math. J., 10 (1960), pp. 359–379 On the topological product of paracompact spaces - Bull. Acad. Polon., 8 (1960), pp. 747–750 Locally complete topological spaces - Dokl. Akad. Nauk SSSR, 137 (1961), pp. 790–792 (in Russian) Applications of complete families of continuous functions to the theory of Q-spaces - Czechoslovak Math. J., 11 (1961), pp. 115–133 Invariance of Gδ-spaces under mappings - Czechoslovak Math. J., 11 (1961), pp. 258–260 On almost real compact spaces - Bull. Acad. Polon., 9 (1961), pp. 247–250 On two problems of W.W. Comfort - Comment. Math. Univ. Carolin., 7 (1966), pp. 139–144 Non-homogeneity of βP- P - Comment. Math. Univ. Carolin., 7 (1966), pp. 705–710 Sums of ultrafilters - Bull. Amer. Math. Soc., 73 (1967), pp. 87–91 Homogeneity problems for extremally disconnected spaces - Comment. Math. Univ. Carolin., 8 (1967), pp. 757–763 Baire sets that are Borelian subspaces - Proc. Roy. Soc. A, 299 (1967), pp. 287–290 On the Suslin-graph theorem - Comment Math. Univ. Carolin., 9 (1968), pp. 243–249 A survey of separable descriptive theory of sets and spaces - Czechoslovak Math. J., 20 (1970), pp. 406–467 A measurable map with analytic domain and metrizable range is quotient - Bull. Amer. Math. Soc., 76 (1970), pp. 1112–1117 Luzin sets are additive - Comment Math. Univ. Carolin., 21 (1980), pp. 527–534 Refinements of perfect maps onto metrizable spaces and an application to Čech-analytic spaces - Topology Appl., 33 (1989), pp. 77–84 Decomposability of completely Suslin additive families - Proc. Amer. Math. Soc., 82 (1981), pp. 359–365 Applications of Luzinian separation principles (non-separable case) - Fund. Math., 117 (1983), pp. 165–185 Analytic and Luzin spaces (non-separable case) - Topology Appl., 19 (1985), pp. 129–156