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Canonical static concept record

Complete metric space

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Summary

A metric space in which every Cauchy sequence converges.

Record metadata

Carrier(s)

Data

Axioms / constraints

Concept sources

Incoming relations (arrows to this concept)

Each relation below ends 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

Metric spaceComplete metric space

Permalink to relation

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

Authored explanation

Require every Cauchy sequence to converge.

How to interpret this relation type

Keep the existing data and select the subclass satisfying an additional law, existence condition, finiteness condition, or other property.

Relation sources

Outgoing relations (arrows from this concept)

Each relation below starts at this concept.

No direct relations are authored in this direction.