A note on spaces that are finitely an F-space

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• 作者：Themba Dube ; ^{dubeta@unisa.ac.za" class="auth_mail" title="E-mail the corresponding author} ; Jissy Nsonde Nsayi ^{nsondj@unisa.ac.za" class="auth_mail" title="E-mail the corresponding author}
• 关键词：54E17 ; 13A15 ; 18A40 ; 06D22
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 April 2016
• 年：2016
• 卷：202
• 期：Complete
• 页码：356-365
• 全文大小：323 K

文摘

A Tychonoff space X is finitely an F-space if βX is expressible as a union of finitely many closed F-spaces. Larson [13] has shown that, for normal spaces X, the property of being finitely an F  -space can be characterized in terms of algebraic properties of the ring C(X)$C(X)$. By extending this notion to locales, we show that the normality restriction can actually be dropped, even in spaces, and thus sharpen Larson's result.