Please use this identifier to cite or link to this item: http://hdl.handle.net/10995/102029
Title: Application of selection principles in the study of the properties of function spaces
Authors: Osipov, A. V.
Issue Date: 2018
Publisher: Springer Netherlands
Citation: Osipov A. V. Application of selection principles in the study of the properties of function spaces / A. V. Osipov. — DOI 10.1007/s10474-018-0800-4 // Acta Mathematica Hungarica. — 2018. — Vol. 154. — Iss. 2. — P. 362-377.
Abstract: For a Tychonoff space X, we denote by Cp(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 Cp(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 Cp(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. © 2018, Akadémiai Kiadó, Budapest, Hungary.
URI: http://hdl.handle.net/10995/102029
Access: info:eu-repo/semantics/openAccess
SCOPUS ID: 85042353940
PURE ID: 7026390
7ab6f527-69d1-499b-a424-4404068a11bd
ISSN: 2365294
DOI: 10.1007/s10474-018-0800-4
Appears in Collections:Научные публикации, проиндексированные в SCOPUS и WoS CC

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