-
belongs to at
least one of the
subsets U α {\displaystyle U_{\alpha }} . A
subcover of a
cover of a set is a
subset of the
cover that also
covers the set....
- of X has a
finite subcover. X has a sub-base such that
every cover of the space, by
members of the sub-base, has a
finite subcover (Alexander's sub-base...
- and
bounded S is compact, that is,
every open
cover of S has a
finite subcover. The
history of what
today is
called the Heine–Borel
theorem starts in...
-
countable subcover. The Lindelöf
property is a
weakening of the more
commonly used
notion of compactness,
which requires the
existence of a
finite subcover. A...
- is
called countably compact if
every countable open
cover has a
finite subcover. A
topological space X is
called countably compact if it
satisfies any...
- {\displaystyle X} by
elements from S {\displaystyle {\mathcal {S}}} has a
finite subcover, then X {\displaystyle X} is compact. The
converse to this
theorem also...
- X} , and
countably compact if
every countable open
cover has a
finite subcover. In a
metric space, the
notions of
sequential compactness,
limit point...
-
finite subcover. Some
authors call
these spaces quasicompact and
reserve compact for
Hausdorff spaces where every open
cover has
finite subcover. Compact...
-
space is a
space in
which every open
cover of the
space contains a
finite subcover. The
methods of
compactification are various, but each is a way of controlling...
- Heine–Borel
theorem I is compact,
implying that this
covering admits a
finite subcover U1, ..., UJ.
There exists an
integer K such that each open
interval Uj...
