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Universally closed implies proper for locales
It is well known that:
Theorem.
For a locale (resp. topological space) $X$, the following are equivalent:
$X$ is compact, i.e. every open cover of $X$ has a finite subcover.
For every locale (resp. ...
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2
votes
1
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Relative Compactness vs Way Below in Locally Compact Hausdorff Spaces
Let $Y$ be a subset of a locally compact Hausdorff topological space $X$ and consider the following properties.
$\overline{Y}$ is compact.
Every open cover of $X$ has a finite subcover of $Y$.
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