TY - JOUR
AU - Karlova, Olena
PY - 2015/02/02
Y2 - 2024/11/08
TI - On C-embedded subspaces of the Sorgenfrey plane
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 16
IS - 1
SE -
DO - 10.4995/agt.2015.3161
UR - https://polipapers.upv.es/index.php/AGT/article/view/3161
SP - 65-74
AB - 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.
ER -