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Abstract

We introduce the notion of maximal μ-open and minimal μ-closed sets in a generalized topological space. We also investigate some of their fundamental properties.

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Abstract  

Some characterizations of S-paracompact spaces are given. We introduce a class of S-expandable spaces and study topological properties of S-expandable spaces.

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Abstract  

We introduce new classes of sets called Λg-closed sets and Λg-open sets in topological spaces. We also investigate several properties of such sets. It turns out that Λg-closed sets and Λg-open sets are weaker forms of closed sets and open sets, respectively and stronger forms of g-closed sets and g-open sets, respectively.

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Abstract

With a slight modification of a previous argument due to Schechter, we show that the Axiom of Choice is equivalent to the following topological statement: “If a product of a non-empty family of sets is closed in a topological (Tychonoff) product, then at least one of the factors is closed”. We also discuss the case on which one adds the hypothesis that the closed product of sets is a non-empty set.

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