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arXiv · 1904.00322

A note on the tightness of $G_\delta$-modifications

Toshimichi Usuba
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Abstract

We construct a normal countably tight $T_1$ space $X$ with $t(X_\delta) >2^\omega$. This is an answer to the question posed by Dow-Juh\'asz-Soukup-Szentmikl\'ossy-Weiss. We also show that if the continuum is not so large, then the tightness of $G_\delta$-modifications of countably tight spaces can be arbitrary large up to the least $\omega_1$-strongly compact cardinal.

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Toshimichi Usuba. 2019-03-31. A note on the tightness of $G_\delta$-modifications. https://arxiv.org/abs/1904.00322

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