Application of selection principles in the study of the properties of function spaces View Full Text


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Article Info

DATE

2018-04

AUTHORS

A. V. Osipov

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. 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. More... »

PAGES

362-377

References to SciGraph publications

  • 1970-05. Baire sets in complete topological spaces in UKRAINIAN MATHEMATICAL JOURNAL
  • 2005-11. On Sequential Separability in MATHEMATICAL NOTES
  • 2006. Some New Directions in Infinite-combinatorial Topology in SET THEORY
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    http://scigraph.springernature.com/pub.10.1007/s10474-018-0800-4

    DOI

    http://dx.doi.org/10.1007/s10474-018-0800-4

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    https://app.dimensions.ai/details/publication/pub.1101179082


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