The Rothberger property on
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- 作者：Daniel Bernal-Santos1 ; shen_woo@me.com" class="auth_mail" title="E-mail the corresponding author
- 关键词：primary ; 54C35 ; 54D35 ; 03G10 ; secondary ; 54D45 ; 54C45
- 刊名：Topology and its Applications
- 出版年：2015
- 出版时间：December 2015
- 年：2015
- 卷：196
- 期：part_PA
- 页码：106-119
- 全文大小：422 K
文摘
In this paper we analyze the Rothberger property on Cp(X,2). A space X is said to have the Rothberger property (or simply X is Rothberger ) if for every sequence 
of open covers of X , there exists Un∈Un for each n∈ω such that 80572" title="Click to view the MathML source">X=⋃n∈ωUn. We show the following: (1) if Cp(X,2) is Rothberger, then X is pseudocompact; (2) for every pseudocompact Sokolov space X with t⁎(X)≤ω, Cp(X,2) is Rothberger; and (3) assuming CH (the continuum hypothesis) there is a maximal almost disjoint family A for which the space Cp(Ψ(A),2) is Rothberger. Moreover, we characterize the Rothberger property on Cp(L,2) when L is a GO-space.
of open covers of X , there exists Un∈Un for each n∈ω such that 80572" title="Click to view the MathML source">X=⋃n∈ωUn. We show the following: (1) if Cp(X,2) is Rothberger, then X is pseudocompact; (2) for every pseudocompact Sokolov space X with t⁎(X)≤ω, Cp(X,2) is Rothberger; and (3) assuming CH (the continuum hypothesis) there is a maximal almost disjoint family A for which the space Cp(Ψ(A),2) is Rothberger. Moreover, we characterize the Rothberger property on Cp(L,2) when L is a GO-space.