Lindelöf P-spaces need not be Sokolov-Reference-Cited by-同舟云学术

Lindelöf P-spaces need not be Sokolov

Published:2017-02-01 Issue:1 Volume:67 Page:227-234
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Tkachuk Vladimir V.¹

Affiliation:

1. Departamento de Matemáticas Universidad Autónoma Metropolitana Av. San Rafael Atlixco, 186 Col. Vicentina, Iztapalapa Mexico City Mexico

Abstract

Abstract We show that for every Lindelöf P-space a weaker version of the Sokolov property holds. Besides, if K is a scattered Eberlein compact space and X is obtained from K by declaring open all Gδ -subsets of K, then X is monotonically Sokolov. The proof of this statement uses the fact that every Lindelöf subspace of a scattered Eberlein compact space must be σ-compact; this result seems to be interesting in itself. We also give an example of a Lindelöf P-space X such that Cp (X) has uncountable extent. In particular, neither X nor Cp (X) has the Sokolov property.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2016-0262/pdf

Reference13 articles.

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4. Leiderman, A. G.: On Properties of Spaces of Continuous Functions. Cardinal Invariants and Mappings of Topological Spaces (in Russian), Izhevsk, 1984, pp. 50–54.

5. Rojas-Hernandez, R.—Tkachuk, V. V.: A monotone version of the Sokolov property and monotone retractability in function spaces, J. Math. Anal. Appl. 412 (2014), 125–137.

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