Compact metrizable space
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 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 | ||||
| compact space | Compact Hausdorff space|FULL LIST, MORE INFO | |||
| completely metrizable space | ||||
| compact Hausdorff space | |FULL LIST, MORE INFO |