Topological countability in Brelot potential theory

@article{Armstrong1974,
abstract = {Let $U$ be a domain of type $H$ in a Brelot potential theory. A compact $K$ in $U$ is a $G_\delta $ in $U$ iff $U-K$ has at most countably many components. If $F$ is a relatively closed locally polar subset of $U$, any $G_\delta $ in $F$ is a $G_\delta $ in $U$. If $V$ is a domain in $U$, all Borel subsets of $\partial V\cap U$ are Baire even if $\partial V\cap U$ is not metrizable. The known results concerning equivalences between weak thinness, thinness, and strong thinness of a set $A$ at a point $x\notin A$ are extended from the case where $\lbrace x\rbrace $ is a $G_\delta $ to the cases in which $A$ meets only countably many components of $U-\lbrace x\rbrace $ or is $K$-analytic.},
author = {Armstrong, Thomas E.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {3},
pages = {15-36},
publisher = {Association des Annales de l'Institut Fourier},
title = {Topological countability in Brelot potential theory},
url = {http://eudml.org/doc/74182},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Armstrong, Thomas E.
TI - Topological countability in Brelot potential theory
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 3
SP - 15
EP - 36
AB - Let $U$ be a domain of type $H$ in a Brelot potential theory. A compact $K$ in $U$ is a $G_\delta $ in $U$ iff $U-K$ has at most countably many components. If $F$ is a relatively closed locally polar subset of $U$, any $G_\delta $ in $F$ is a $G_\delta $ in $U$. If $V$ is a domain in $U$, all Borel subsets of $\partial V\cap U$ are Baire even if $\partial V\cap U$ is not metrizable. The known results concerning equivalences between weak thinness, thinness, and strong thinness of a set $A$ at a point $x\notin A$ are extended from the case where $\lbrace x\rbrace $ is a $G_\delta $ to the cases in which $A$ meets only countably many components of $U-\lbrace x\rbrace $ or is $K$-analytic.
LA - eng
UR - http://eudml.org/doc/74182
ER -