On C-embedded subspaces of the Sorgenfrey plane

Olena Karlova

doi:10.4995/agt.2015.3161

Authors

Olena Karlova Chernivtsi National University

DOI:

https://doi.org/10.4995/agt.2015.3161

Keywords:

$C^*$-embedded, $C$-embedded, the Sorgenfrey plane.

Abstract

We show that for a subspace $E\subseteq\{(x,-x):x\in\mathbb R\}$ of the Sorgenfrey plane $\mathbb S^2$ the following conditions are equivalent: (i) $E$ is $C$-embedded in $\mathbb S^2$; (ii) $E$ is $C^*$-embedded in $\mathbb S^2$; (iii) $E$ is a countable $G_\delta$-subspace of $\rr$ and (iv) $E$ is a countable functionally closed subspace of $\ss$. We also prove that $\mathbb S^2$ is not a $\delta$-normally separated space.

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Author Biography

Olena Karlova, Chernivtsi National University

Assistant professor of the Department of Mathematical Analysis

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