- in the
field of topology, a
Hausdorff topological space is said to be
hemicompact if it has a
sequence of
compact subsets such that
every compact subset...
-
compact since Rω is a
topological group that is also a
Baire space.
Every hemicompact space is σ-compact. The converse, however, is not true; for example,...
- The
hemicompact property is
intermediate between exhaustible by
compact sets and σ-compact.
Every space exhaustible by
compact sets is
hemicompact and...
- sup{d( f (x), g(x)) : x in X}, for f , g in C(X, Y). More generally, if X is
hemicompact, and Y metric, the compact-open
topology is
metrizable by the construction...
- an
exhaustion by
compact sets (that is, X {\displaystyle X} must be
hemicompact). However, it can be
generalized as follows: let X {\displaystyle X}...
- if it is
closed in
every Hausdorff space containing it.
Hemicompact A
space is
hemicompact, if
there is a
sequence of
compact subsets so that
every compact...
