On $\sigma$-countably tight spaces

István Juhász; Jan van Mill

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arXiv · 1607.00517

On $\sigma$-countably tight spaces

István Juhász·Jan van Mill

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Abstract

Extending a result of R. de la Vega, we prove that an infinite homogeneous compactum has cardinality $\mathfrak{c}$ if either it is the union of countably many dense or finitely many arbitrary countably tight subspaces. The question if every infinite homogeneous and $\sigma$-countably tight compactum has cardinality $\mathfrak{c}$ remains open. We also show that if an arbitrary product is $\sigma$-countably tight then all but finitely many of its factors must be countably tight.

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István Juhász, Jan van Mill. 2016-07-02. On $\sigma$-countably tight spaces. https://arxiv.org/abs/1607.00517

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