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arXiv · 1112.0883

Weak extent, submetrizability and diagonal degrees

D. Basile·A. Bella·G. J. Ridderbos
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Abstract

We show that if $X$ has a zero-set diagonal and $X^2$ has countable weak extent, then $X$ is submetrizable. This generalizes earlier results from Martin and Buzyakova. Furthermore we show that if $X$ has a regular $G_δ$-diagonal and $X^2$ has countable weak extent, then $X$ condenses onto a second countable Hausdorff space. We also prove several cardinality bounds involving various types of diagonal degree.

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D. Basile, A. Bella, G. J. Ridderbos. 2011-12-05. Weak extent, submetrizability and diagonal degrees. https://arxiv.org/abs/1112.0883

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