In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more obvious, topology called the box topology, which can also be given to a product space and which agrees with the product topology when the product is over only finitely many spaces.

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  • In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more obvious, topology called the box topology, which can also be given to a product space and which agrees with the product topology when the product is over only finitely many spaces. However, the product topology is "correct" in that it makes the product space a categorical product of its factors, whereas the box topology is too fine; this is the sense in which the product topology is "natural".
  • In der Topologie ist die Produkttopologie die „natürlichste“ Topologie, die ein kartesisches Produkt von topologischen Räumen selbst zu einem topologischen Raum macht.
  • La topologie produit est une topologie définie sur un produit d'espaces topologiques. C'est de manière générale la topologie faible associée aux projections de l'espace produit vers chacun de ses facteurs: autrement dit c'est la topologie la moins fine rendant les projections continues.
  • La topologia prodotto è una topologia naturale definita sul prodotto cartesiano di alcuni spazi topologici.
  • In de topologie, een tak van de wiskunde, is de producttopologie een topologische structuur op het Cartesisch product van topologische ruimten.
  • Topologia Tichonowa to pojęcie w topologii odnoszące się do sposobu wprowadzania rodziny zbiorów otwartych na iloczynie kartezjańskim przestrzeni topologicznych.
  • A topologia produto é a menor topologia em um produto de espaços topológicos que torna cada projeção canônica uma função contínua. Deve-se notar que essa definição é boa porque, como na topologia discreta toda função é contínua, estamos definindo a topologia produto como a interseção de um número não-vazio de topologias, e a interseção de topologias é uma topologia.
  • 拓扑学和数学的相关领域中，积空间是指一族拓扑空间的卡积，并配备了一个称为积拓扑的自然的拓扑结构。
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  • In topology and related areas of mathematics, a product space is the cartesian product of a family of topological spaces equipped with a natural topology called the product topology. This topology differs from another, perhaps more obvious, topology called the box topology, which can also be given to a product space and which agrees with the product topology when the product is over only finitely many spaces.
  • In der Topologie ist die Produkttopologie die „natürlichste“ Topologie, die ein kartesisches Produkt von topologischen Räumen selbst zu einem topologischen Raum macht.
  • La topologie produit est une topologie définie sur un produit d'espaces topologiques. C'est de manière générale la topologie faible associée aux projections de l'espace produit vers chacun de ses facteurs: autrement dit c'est la topologie la moins fine rendant les projections continues.
  • La topologia prodotto è una topologia naturale definita sul prodotto cartesiano di alcuni spazi topologici.
  • In de topologie, een tak van de wiskunde, is de producttopologie een topologische structuur op het Cartesisch product van topologische ruimten.
  • Topologia Tichonowa to pojęcie w topologii odnoszące się do sposobu wprowadzania rodziny zbiorów otwartych na iloczynie kartezjańskim przestrzeni topologicznych.
  • A topologia produto é a menor topologia em um produto de espaços topológicos que torna cada projeção canônica uma função contínua. Deve-se notar que essa definição é boa porque, como na topologia discreta toda função é contínua, estamos definindo a topologia produto como a interseção de um número não-vazio de topologias, e a interseção de topologias é uma topologia.
  • 拓扑学和数学的相关领域中，积空间是指一族拓扑空间的卡积，并配备了一个称为积拓扑的自然的拓扑结构。
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  • Product topology
  • Produkttopologie
  • Topologie produit
  • Topologia prodotto
  • Producttopologie
  • Topologia Tichonowa
  • Topologia produto
  • 积空间
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