About: Disjoint union (topology)

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In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. Roughly speaking, in the disjoint union the given spaces are considered as part of a single new space where each looks as it would alone and they are isolated from each other.

Attributes	Values
rdfs:label	Disjoint union (topology) (en) 直和 (位相空間論) (ja)
rdfs:comment	位相空間論および関連した数学の分野において、位相空間の族の非交和（ひこうわ、英: disjoint union）または直和（ちょくわ、英: direct sum）とは、台集合の非交和（集合の直和）に非交和位相 (disjoint union topology) と呼ばれるを入れることによって形成される位相空間を言う。乱暴な言い方をすれば、2つ以上の空間をそれぞれ個々の空間と見なすと同時に、すべて一緒にした一つの空間としても考えるということである。非交和空間は積空間の構成の圏論的双対となるため、余積 (coproduct) とも呼ばれる。そのほかにも、自由合併 (free union)、自由和 (free sum)、位相和 (topological sum) などの呼び名もある。 (ja) In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. Roughly speaking, in the disjoint union the given spaces are considered as part of a single new space where each looks as it would alone and they are isolated from each other. (en)
foaf:depiction
dcterms:subject	General topology
Wikipage page ID	1564380 (xsd:integer)
Wikipage revision ID	1020228955 (xsd:integer)
Link from a Wikipage to another Wikipage	Product topology Topological embedding Topological union Homeomorphic Mathematics General topology Coproduct Commutative diagram Hausdorff space General topology T0 space Discrete space Disjoint union Final topology Continuous function (topology) If and only if Iff Indexed family Open and closed maps Open set Category of topological spaces Subspace topology Universal property Natural topology Topological space T1 space Preimage Finest topology Categorical dual Disconnected (topology) Quotient topology Product space Subspace (topology)
sameAs	Disjoint union (topology) Disjoint union (topology) Disjoint union (topology) Disjoint union (topology)
dbp:wikiPageUsesTemplate	dbt:Unreferenced
thumbnail	wiki-commons:Special:FilePath/Coproduct-02.png?width=300
has abstract	In general topology and related areas of mathematics, the disjoint union (also called the direct sum, free union, free sum, topological sum, or coproduct) of a family of topological spaces is a space formed by equipping the disjoint union of the underlying sets with a natural topology called the disjoint union topology. Roughly speaking, in the disjoint union the given spaces are considered as part of a single new space where each looks as it would alone and they are isolated from each other. The name coproduct originates from the fact that the disjoint union is the categorical dual of the product space construction. (en) 位相空間論および関連した数学の分野において、位相空間の族の非交和（ひこうわ、英: disjoint union）または直和（ちょくわ、英: direct sum）とは、台集合の非交和（集合の直和）に非交和位相 (disjoint union topology) と呼ばれるを入れることによって形成される位相空間を言う。乱暴な言い方をすれば、2つ以上の空間をそれぞれ個々の空間と見なすと同時に、すべて一緒にした一つの空間としても考えるということである。非交和空間は積空間の構成の圏論的双対となるため、余積 (coproduct) とも呼ばれる。そのほかにも、自由合併 (free union)、自由和 (free sum)、位相和 (topological sum) などの呼び名もある。 (ja)
gold:hypernym	Space
prov:wasDerivedFrom	wikipedia-en:Disjoint_union_(topology)?oldid=1020228955&ns=0
page length (characters) of wiki page	3893 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Disjoint_union_(topology)
is Link from a Wikipage to another Wikipage of	Coproduct in the category of topological spaces Topological disjoint sum Topological sum Coproduct Compactly generated space Wedge sum Mapping cylinder Noncommutative topology Adjunction space Join (topology) Local homeomorphism Locally compact space Locally connected space Abstract analytic number theory Coherent topology CW complex Fiber bundle construction theorem Final topology Coproduct topology Category of topological spaces Topological manifold Disjoint union topology List of topologies Polyadic space Totally disconnected space Strong topology Free sum Direct sum (topology) Direct sum topology
is Wikipage redirect of	Coproduct in the category of topological spaces Topological disjoint sum Topological sum Coproduct topology Disjoint union topology Free sum Direct sum (topology) Direct sum topology
is foaf:primaryTopic of	wikipedia-en:Disjoint_union_(topology)

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