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Generalized metric space — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Generalized_metric_space
License (as archived): CC-BY-SA-4.0
Archived: 2026-11-07T18:23:27.794Z
SHA-256 of the archived text: c94221340dd71b78d39e96adeb9e32b196260f911f0d97a0b80a0b5a481c3f82
Stable URL of this page: https://metraipolis.com/documento/dc_4e9ec17d44ff

How to cite

Generalized metric space — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Generalized_metric_space (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_4e9ec17d44ff (Metraipolis archive dc_4e9ec17d44ff, sha256 c94221340dd71b78d39e96adeb9e32b196260f911f0d97a0b80a0b5a481c3f82)

BibTeX

@misc{dc4e9ec17d44ff,
  title = {Generalized metric space — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Generalized_metric_space},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_4e9ec17d44ff; sha256 c94221340dd71b78d39e96adeb9e32b196260f911f0d97a0b80a0b5a481c3f82},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Generalized_metric_space. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In mathematics, specifically in category theory, a generalized metric space is a metric space but without some properties, such as symmetry. Precisely, it is a category enriched over [ 0 , ∞ ] {\displaystyle [0,\infty ]} , the one-point compactification of R {\displaystyle \mathbb {R} } . The notion was introduced in 1973 by William Lawvere who noticed that a metric space can be viewed as a particular kind of category. The categorical point of view is useful since by Yoneda's lemma, a generalized metric space can be embedded into a much larger category in which, for instance, one can construct the Cauchy completion of the space.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «category theory»).
Fonte: Wikipedia in inglese, voce «Generalized metric space» — https://en.wikipedia.org/wiki/Generalized_metric_space
Wikidata Q131320009 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q131320009
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Generalized_metric_space?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1383352577, consultata il 2026-11-07T18:18:31.656Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 2a191638dbabd7ee3efd159edc810d39056f7260984814820cc89747036c635d