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On compact* spaces and compactifications
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The space
β
X
\beta X
of
Z
Z
-ultrafilters on
X
X
with the standard filter space topology is shown to be compact*. Without considering the reflection associated with compact* spaces, we also prove that products of compact* spaces are compact*, in response to a request for a direct proof.
American Mathematical Society (AMS)
Title: On compact* spaces and compactifications
Description:
The space
β
X
\beta X
of
Z
Z
-ultrafilters on
X
X
with the standard filter space topology is shown to be compact*.
Without considering the reflection associated with compact* spaces, we also prove that products of compact* spaces are compact*, in response to a request for a direct proof.
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