Zdeněk Frolík

Zdeněk Frolík in 1971

Zdeněk Frolík (March 10, 1933 – May 3, 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.^[1]

Two classes of topological spaces are given Frolík's name: the class P of all spaces $X$ such that $X \times Y$ is pseudocompact for every pseudocompact space $Y$,^[2] and the class C of all spaces $X$ such that $X \times Y$ is countably compact for every countably compact space $Y$.^[3]

Frolík prepared his Ph.D. thesis under the supervision of Miroslav Katetov and Eduard Čech.^[4]

^{[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27]}

References

1. Zdeněk Frolík 1933–1989, Mirek Husek, Jan Pelant, Topology and its Applications, Volume 44, issues 1–3, 22 May 1992, pages 11–17,(access on subscription).
2. Vaughan, Jerry E., On Frolík's characterization of class P. Czechoslovak Mathematical Journal, vol. 44 (1994), issue 1, pp. 1-6, freely available.
3. J.E. Vaughan, Countably compact and sequentially compact spaces. Handbook of Set-theoretic Topology, K. Kunen and J. Vaughan (ed.), North-Holland, Amsterdam, 1984.
4. Zdeněk Frolík on the Mathematics Genealogy Project.
5. Generalizations of compact and Lindelöf spaces - Czechoslovak Math. J., 9 (1959), pp. 172–217 (in Russian, English summary)
6. The topological product of countably compact spaces - Czechoslovak Math. J., 10 (1960), pp. 329–338
7. The topological product of two pseudocompact spaces - Czechoslovak Math. J., 10 (1960), pp. 339–349
8. Generalizations of the Gδ-property of complete metric spaces - Czechoslovak Math. J., 10 (1960), pp. 359–379
9. On the topological product of paracompact spaces - Bull. Acad. Polon., 8 (1960), pp. 747–750
10. Locally complete topological spaces - Dokl. Akad. Nauk SSSR, 137 (1961), pp. 790–792 (in Russian)
11. Applications of complete families of continuous functions to the theory of Q-spaces - Czechoslovak Math. J., 11 (1961), pp. 115–133
12. Invariance of Gδ-spaces under mappings - Czechoslovak Math. J., 11 (1961), pp. 258–260
13. On almost real compact spaces - Bull. Acad. Polon., 9 (1961), pp. 247–250
14. On two problems of W.W. Comfort - Comment. Math. Univ. Carolin., 7 (1966), pp. 139–144
15. Non-homogeneity of βP- P - Comment. Math. Univ. Carolin., 7 (1966), pp. 705–710
16. Sums of ultrafilters - Bull. Amer. Math. Soc., 73 (1967), pp. 87–91
17. Homogeneity problems for extremally disconnected spaces - Comment. Math. Univ. Carolin., 8 (1967), pp. 757–763
18. Baire sets that are Borelian subspaces - Proc. Roy. Soc. A, 299 (1967), pp. 287–290
19. On the Suslin-graph theorem - Comment Math. Univ. Carolin., 9 (1968), pp. 243–249
20. A survey of separable descriptive theory of sets and spaces - Czechoslovak Math. J., 20 (1970), pp. 406–467
21. A measurable map with analytic domain and metrizable range is quotient - Bull. Amer. Math. Soc., 76 (1970), pp. 1112–1117
22. Luzin sets are additive - Comment Math. Univ. Carolin., 21 (1980), pp. 527–534
23. Refinements of perfect maps onto metrizable spaces and an application to Čech-analytic spaces - Topology Appl., 33 (1989), pp. 77–84
24. Decomposability of completely Suslin additive families - Proc. Amer. Math. Soc., 82 (1981), pp. 359–365
25. Applications of Luzinian separation principles (non-separable case) - Fund. Math., 117 (1983), pp. 165–185
26. Analytic and Luzin spaces (non-separable case) - Topology Appl., 19 (1985), pp. 129–156
27. Other references here