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- Title
APPLICATION OF SELECTION PRINCIPLES IN THE STUDY OF THE PROPERTIES OF FUNCTION SPACES.
- Authors
OSIPOV, A. V.
- Abstract
For a Tychonoff space X, we denote by C p (X) the space of all real-valued continuous functions on X with the topology of pointwise convergence. In this paper we prove that: If every finite power of X is Lindelöf then C p (X) is strongly sequentially separable iff X is γ-set. Bα(X) (= functions of Baire class α (1<α≤ω1) on a Tychonoff space X with the pointwise topology) is sequentially separable iff there exists a Baire isomorphism class α from a space X onto a σ-set. Bα(X) is strongly sequentially separable iff iw(X)=ℵ0 and X is a Zα-cover γ-set for 0<α≤ω1. There is a consistent example of a set of reals X such that C p (X) is strongly sequentially separable but B1(X) is not strongly sequentially separable. B(X) is sequentially separable but is not strongly sequentially separable for a b-Sierpiński set X.
- Subjects
FUNCTION spaces; TOPOLOGY; BAIRE spaces; ISOMORPHISM (Mathematics); STOCHASTIC convergence
- Publication
Acta Mathematica Hungarica, 2018, Vol 154, Issue 2, p362
- ISSN
0236-5294
- Publication type
Article
- DOI
10.1007/s10474-018-0800-4