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Box topology — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Box_topology
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-06T12:52:35.745Z
SHA-256 of the archived text: dc624a13d849c353895e9bba9bca1a5e5577190805f11347bc74f3b000696157
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Box topology — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Box_topology (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_49db38bd349e (Metraipolis archive dc_49db38bd349e, sha256 dc624a13d849c353895e9bba9bca1a5e5577190805f11347bc74f3b000696157)

BibTeX

@misc{dc49db38bd349e,
  title = {Box topology — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Box_topology},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_49db38bd349e; sha256 dc624a13d849c353895e9bba9bca1a5e5577190805f11347bc74f3b000696157},
  year = {2026}
}

Archived text

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

In topology, the cartesian product of topological spaces can be given several different topologies. One of the more natural choices is the box topology, where a base is given by the Cartesian products of open sets in the component spaces. Another possibility is the product topology, where a base is also given by the Cartesian products of open sets in the component spaces, but only finitely many of which can be unequal to the entire component space. While the box topology has a somewhat more intuitive definition than the product topology, it satisfies fewer desirable properties. In particular, if all the component spaces are compact, the box topology on their Cartesian product will not necessarily be compact, although the product topology on their Cartesian product will always be compact. In general, the box topology is finer than the product topology, although the two agree in the case of finite direct products (or when all but finitely many of the factors are trivial).

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «topology»).
Fonte: Wikipedia in inglese, voce «Box topology» — https://en.wikipedia.org/wiki/Box_topology
Wikidata Q4951625: «mathematical concept» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q4951625
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Box_topology?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 1370094847, consultata il 2026-10-06T11:08:50.271Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 644b6d970643f9d55d84aab07d8e0ae11a19be4fea4b4f4a8d0f6556655759bc