2021
DOI: 10.48550/arxiv.2103.05139
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On Urysohn's Lemma for generalized topological spaces in ZF

Abstract: A strong generalized topological space is an ordered pair X = X, T such that X is a set and T is a collection of subsets of X such that ∅, X ∈ T and T is stable under arbitrary unions. A necessary and sufficient condition for a strong generalized topological space X to satisfy Urysohn's lemma or its appropriate variant is shown in ZF. Notions of a U-normal and an effectively normal generalized topological space are introduced. It is observed that, in ZF + DC, every U-normal generalized topological space satisf… Show more

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