Download Alexandrov one-point compactification

Alexandrov one-point compactification∗
yark†
2013-03-21 16:20:27
The Alexandrov one-point compactification of a non-compact topological
space X is obtained by adjoining a new point ∞ and defining the topology
on X ∪ {∞} to consist of the open sets of X together with the sets of the form
U ∪ {∞}, where U is an open subset of X with compact complement.
With this topology, X ∪{∞} is always compact. Furthermore, it is Hausdorff
if and only if X is Hausdorff and locally compact.
∗ hAlexandrovOnepointCompactificationi
created: h2013-03-21i by: hyarki version:
h34515i Privacy setting: h1i hDefinitioni h54D35i
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