Compact metrizable space

From Topospaces
Jump to: navigation, search

Definition

A topological space is termed compact metrizable if it is compact and metrizable, or eqiuvalently, if it can be given the structure of a compact metric space.

This article defines a property of topological spaces: a property that can be evaluated to true/false for any topological space|View a complete list of properties of topological spaces

This article describes a property of topological spaces obtained as a conjunction of the following two properties: compact space and metrizable space

Relation with other properties

Weaker properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
supercompact space there is a subbasis of open subsets such that any open cover using that subbasis has a subcover using at most two subsets
compact space Compact Hausdorff space|FULL LIST, MORE INFO
completely metrizable space
compact Hausdorff space |FULL LIST, MORE INFO