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arXiv · 1411.3173

On $\alpha$-embedded subsets of products

Olena Karlova·Volodymyr Mykhaylyuk
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Abstract

We prove that every continuous function $f:E\to Y$ depends on countably many coordinates, if $E$ is an $(\aleph_1,\aleph_0)$-invariant pseudo-$\aleph_1$-compact subspace of a product of topological spaces and $Y$ is a space with a regular $G_\delta$-diagonal. Using this fact for any $\alpha<\omega_1$ we construct an $(\alpha+1)$-embedded subspace of a completely regular space which is not $\alpha$-embedded.

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Olena Karlova, Volodymyr Mykhaylyuk. 2014-11-12. On $\alpha$-embedded subsets of products. https://doi.org/10.1007/s40879-014-0018-0

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