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Topological countability in Brelot potential theory

Thomas E. Armstrong — 1974

Annales de l'institut Fourier

Let $U$ be a domain of type $H$ in a Brelot potential theory. A compact $K$ in $U$ is a $G_{δ}$ in $U$ iff $U - K$ has at most countably many components. If $F$ is a relatively closed locally polar subset of $U$ , any $G_{δ}$ in $F$ is a $G_{δ}$ 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 ${x}$ is a $G_{δ}$ to the cases in which $A$ meets only countably...

The Poulsen simplex is not a tensor product.

Armstrong, Thomas E. — 1984

International Journal of Mathematics and Mathematical Sciences

Page 1

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