Definition of Subcover. Meaning of Subcover. Synonyms of Subcover

- {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...
- 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...
- 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...
- {\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...
- 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...
- 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...
- countable dense subset) and Lindelöf (every open cover has a countable subcover). The reverse implications do not hold. For example, the lower limit topology...
- (Theorem): Take O ∗ {\displaystyle {\mathcal {O}}^{*}\,} a locally finite subcover of the refinement cover: { V  open  : ( ∃ U ∈ O ) V ¯ ⊆ U } {\displaystyle...