On a certain generalization of $W$-spaces

Martin Doležal; Warren B. Moors

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arXiv · 1705.04037

On a certain generalization of $W$-spaces

Martin Doležal·Warren B. Moors

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Abstract

We present a simple generalization of $W$-spaces introduced by G. Gruenhage. We show that this generalization leads to a strictly larger class of topological spaces which we call $\widetilde W$-spaces, and we provide several applications. Namely, we use the notion of $\widetilde W$-spaces to provide sufficient conditions for the product of two spaces to be a Baire space, for a semitopological group to be a topological group, or for a separately continuous function to be continuous at the points of a certain large set.

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Martin Doležal, Warren B. Moors. 2017-05-11. On a certain generalization of $W$-spaces. https://arxiv.org/abs/1705.04037

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