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Compact metric space

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Summary

A metric space that is compact in its metric topology.

Record metadata

Carrier(s)

Data

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends at this concept.

compact + metric(construction junction)Compact metric space

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Require the metric topology to be compact.

How to interpret this relation type

Feed several structures into a construction junction and impose compatibility between them.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

Compact metric spaceComplete metric space

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This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Every compact metric space is complete.

How to interpret this relation type

Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.

Relation sources

Compact metric spaceSeparable metric space

Permalink to relation

This is an authored directed relation from the source endpoint to the target endpoint.

Authored explanation

Every compact metric space has a countable dense subset.

How to interpret this relation type

Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.

Relation sources