https://link.springer.com/10.1007%2Fs10474-018-0800-4
2018-04
Application of selection principles in the study of the properties of function spaces
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.
true
362-377
2019-04-11T09:34
en
research_article
https://scigraph.springernature.com/explorer/license/
articles
2018-04-01
2
A. V.
Osipov
Springer Nature - SN SciGraph project
154
doi
10.1007/s10474-018-0800-4
Krasovskii Institute of Mathematics and Mechanics, Ural Federal University, Ural State University of Economics, Yekaterinburg, Russia
Ural Federal University
1588-2632
0236-5294
Acta Mathematica Hungarica
readcube_id
811846ae10a31c2e2a8a3c19bfaa665ed5534b62ac328c7bfd95fee83ce23e77
Information Systems
dimensions_id
pub.1101179082
Information and Computing Sciences