-
mathematical field of
general topology, a
topological space is said to be
metacompact if
every open
cover has a point-finite open refinement. That is, given...
- a
compact space is paracompact. The
product of a
metacompact space and a
compact space is
metacompact. Both
these results can be
proved by the tube lemma...
- open
cover is
interior preserving. Hence, we have the following:
every metacompact space, and in particular,
every paracompact space, is orthocompact. Useful...
- Carathéodory's
extension theorem Geometric set
cover problem Dimension theory Metacompact space Point-finite
collection Lebesgue,
Henri (1921). "Sur les correspondances...
-
neither compact,
sequentially compact,
countably compact,
paracompact nor
metacompact (although it is orthocompact). However,
since X is hyperconnected, it...
- (or
equivalently that
every open
cover has a
countable refinement);
metacompact: if
every open
cover has a point-finite open refinement; paracompact:...
-
definitions of
paracompact space and
metacompact space, and this is the
reason why
every paracompact space is
metacompact. If a
collection of sets is locally...
-
plane is not
locally compact. The
Moore plane is
countably metacompact but not
metacompact. The fact that this
space Γ {\displaystyle \Gamma } is not...
- sets. If A is not
meagre in X, A is of
second category in X.
Metacompact A
space is
metacompact if
every open
cover has a
point finite open refinement. Metric...
- only
finitely many
members of U . {\displaystyle {\mathcal {U}}.} A
metacompact space is a
topological space in
which every open
cover admits a point-finite...
