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On weakly Baire spaces. (English) Zbl 0747.54008
G. Beer and L. Villar [Southeast Asian Bull. Math. 11, No. 2, 127-133 (1988; Zbl 0665.54019)] define a $$T_ 1$$ space to be weakly Baire if each non-empty open subset of it is uncountable or has an isolated point. The authors of the paper under review expand this concept to all topological spaces by calling a space to be weakly Baire if there are no countable meager open non-empty subsets. They examine this concept under various topological operations (subspaces, products, hyperspaces).
MSC:
 54E52 Baire category, Baire spaces 54B20 Hyperspaces in general topology 54B05 Subspaces in general topology