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Every k-separable Čech-complete space is subcompact
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Every k-separable Čech-complete space is subcompact
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Journal Article
Every k-separable Čech-complete space is subcompact
2015
Overview
We establish that a Čech-complete space
X
must be subcompact if it has a dense subspace representable as the countable union of closed subcompact subspaces of
X
. In particular, if a Čech-complete space contains a dense
σ
-compact subspace then it is subcompact. This result is new even for separable Čech-complete spaces. Furthermore, if
X
is a compact space of countable tightness then
X
\\
A
is subcompact for any countable set
A
⊂
X
. We also show that any
G
δ
-subset of a dyadic compact space is subcompact and give a comparatively simple proof of the fact that
X
\\
A
is subcompact for any linearly ordered compact space
X
and any countable set
A
⊂
X
.
Publisher
Springer Milan,Springer Nature B.V
