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On the topological strength of set-theoretic operations. (English. Russian original) Zbl 0666.54020

Math. USSR, Sb. 63, No. 2, 393-404 (1989); translation from Mat. Sb., Nov. Ser. 135(177), No. 3, 403-413 (1988).
The author introduces the concept of the topological power for set- theoretic operations. The main result of the paper is a criterion for comparing two set-theoretic operations with respect to their topological power, analogous to the one for the absolute power, established by the author earlier [Dokl. Akad. Nauk SSSR 201, 40-43 (1971; Zbl 0239.04003)]. The author also addresses some questions related to a theorem of A. N. Kolmogorov concerning set-theoretical operations [Mat. Sb. 35, 414- 422 (1928)].
Reviewer: D.Repovš

MSC:

54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
03E15 Descriptive set theory
54B20 Hyperspaces in general topology

Citations:

Zbl 0239.04003
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