On C-embedded subspaces of the Sorgenfrey plane

Karlova, Olena ^[1]
1. [1] Chernivtsi National University
  
  Chernivtsi National University
  
  Ucrania
Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 16, Nº. 1, 2015, págs. 65-74
Idioma: inglés
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Resumen
- 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.