- {O}}:A\in {\mathcal {A}}\}} is a
subcover of O . {\displaystyle {\mathcal {O}}.}
Hence the
cardinality of a
subcover of an open
cover can be as small...
- 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...
-
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...
- compact, that is,
every open
cover of S {\displaystyle S} has a
finite subcover S {\displaystyle S} is
closed and bounded. The
history of what
today is...
- {\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...
- Lindelöf. Lindelöf. A
space is Lindelöf if
every open
cover has a
countable subcover. σ-compact. A
space is σ-compact if it is the
union of
countably many compact...
-
uniform covers, X is
totally bounded if
every uniform cover has a
finite subcover. Compact. A
uniform space is
compact if it is
complete and
totally bounded...
- 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...
-
Compact space, a
topological space such that
every open
cover has a
finite subcover Quasi-compact morphism, a
morphism of
schemes for
which the
inverse image...
- X} , and
countably compact if
every countable open
cover has a
finite subcover. In a
metric space, the
notions of
sequential compactness,
limit point...
