Compact metrizable space: Difference between revisions
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| [[Stronger than::compact space]] || || || || | | [[Stronger than::compact space]] || || || || {{intermediate notions short|compact space|compact metrizable space}} | ||
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|[[Stronger than::completely metrizable space]] || || || || | |[[Stronger than::completely metrizable space]] || || || || | ||
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| [[Stronger than::compact Hausdorff space]] || || || || | | [[Stronger than::compact Hausdorff space]] || || || || {{intermediate notions short|compact Hausdorff space|compact metrizable space}} | ||
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Revision as of 18:42, 28 January 2012
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 |