About: Box topology

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In topology, the cartesian product of topological spaces can be given several different topologies. One of the more obvious 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 given by the Cartesian products of open sets in the component spaces, only finitely many of which can be not equal to the entire component space.

Attributes	Values
rdf:type	yago:WikicatTopologicalSpaces yago:Abstraction100002137 yago:Attribute100024264 yago:MathematicalSpace108001685 yago:Set107999699 yago:Space100028651
rdfs:label	Box topology (en) Topologie des boîtes (fr) 상자 위상 (ko)
rdfs:comment	La topologie des boîtes (terme traduit de l'anglais box topology) est une des topologies qu'il est possible d'affecter à un produit d'espaces topologiques . Elle diffère de la topologie dite topologie produit en ce qu'on y considère comme ouverts tous les dès lors que chaque est un ouvert de l'espace correspondant , sans exiger que sauf pour un nombre fini de valeurs de (fr) In topology, the cartesian product of topological spaces can be given several different topologies. One of the more obvious 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 given by the Cartesian products of open sets in the component spaces, only finitely many of which can be not equal to the entire component space. (en)
dct:subject	Topological spaces Operations on structures
Wikipage page ID	954333 (xsd:integer)
Wikipage revision ID	1124119122 (xsd:integer)
Link from a Wikipage to another Wikipage	Cartesian product Product topology Cylinder set Index set Compact space Separable space Connected space Continuum hypothesis Topological spaces Topology J. Arthur Seebach Jr. Operations on structures Base (topology) Hilbert cube Pointwise convergence Counterexample Counterexamples in Topology First countable Trivial topology Continuous function (topology) Paracompact Metrizable Sequence List of topologies Real line Topological space Basis (topology) Finer topology Completely regular Lynn Arthur Steen dbr:Wiktionary:finite
sameAs	Box topology Box topology Box topology Box topology Box topology Box topology Box topology
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:ISBN dbt:Reflist dbt:Planetmath_reference
title	Box topology (en)
urlname	BoxTopology (en)
has abstract	In topology, the cartesian product of topological spaces can be given several different topologies. One of the more obvious 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 given by the Cartesian products of open sets in the component spaces, only finitely many of which can be not equal 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). (en) La topologie des boîtes (terme traduit de l'anglais box topology) est une des topologies qu'il est possible d'affecter à un produit d'espaces topologiques . Elle diffère de la topologie dite topologie produit en ce qu'on y considère comme ouverts tous les dès lors que chaque est un ouvert de l'espace correspondant , sans exiger que sauf pour un nombre fini de valeurs de (fr)
prov:wasDerivedFrom	wikipedia-en:Box_topology?oldid=1124119122&ns=0
page length (characters) of wiki page	7459 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Box_topology
is Link from a Wikipage to another Wikipage of	Product topology Box product Cylinder set General topology Direct product Baire space (set theory) Counterexamples in Topology Cofiniteness Trivial topology List of topologies Box product topology
is Wikipage redirect of	Box product topology
is foaf:primaryTopic of	wikipedia-en:Box_topology

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