Weak extent, submetrizability and diagonal degrees

Details Weak extent, submetrizability and diagonal degrees Weak extent, submetrizability and diagonal degrees

2011-12-05

arxiv.org/abs/1112.0883v1

Mathematics

General Topology

10 pages

Scientific paper

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 $G_\delta$-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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