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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. 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)
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- 7459 (xsd:nonNegativeInteger)
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- 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)
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- Box topology (en)
- Topologie des boîtes (fr)
- 상자 위상 (ko)
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