Quotient space (topology)
In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes). In other words, a subset of a quotient space is open if and only if its preimage under the canonical projection map is open in the original topological space.
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Quotient space (topology)
In topology and related areas of mathematics, the quotient space of a topological space under a given equivalence relation is a new topological space constructed by endowing the quotient set of the original topological space with the quotient topology, that is, with the finest topology that makes continuous the canonical projection map (the function that maps points to their equivalence classes). In other words, a subset of a quotient space is open if and only if its preimage under the canonical projection map is open in the original topological space.
has abstract
Die Quotiententopologie (auch ...... he den Artikel Finaltopologie.
@de
Em topologia, um espaço topoló ...... cuja reunião é um aberto de X.
@pt
En matemàtiques, la topologia ...... ncia sobre un espai topològic.
@ca
En matemáticas, la topología c ...... temático o la banda de Möbius.
@es
En mathématiques, la topologie ...... d'espace topologique quotient.
@fr
In de topologie wordt de const ...... e begrip "aan elkaar plakken".
@nl
In topologia, la topologia quo ...... che chiamato spazio quoziente.
@it
In topology and related areas ...... ive plane as a quotient space.
@en
Фактор-простір — простір класі ...... м відношенням еквівалентності.
@uk
位相空間論およびそれに関連する数学の各分野において、等化空間 ...... 空間から新たな空間を構成する方法の一つとして広く用いられる。
@ja
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Die Quotiententopologie (auch ...... he den Artikel Finaltopologie.
@de
Em topologia, um espaço topoló ...... cuja reunião é um aberto de X.
@pt
En matemàtiques, la topologia ...... ncia sobre un espai topològic.
@ca
En matemáticas, la topología c ...... temático o la banda de Möbius.
@es
En mathématiques, la topologie ...... d'espace topologique quotient.
@fr
In de topologie wordt de const ...... e begrip "aan elkaar plakken".
@nl
In topologia, la topologia quo ...... che chiamato spazio quoziente.
@it
In topology and related areas ...... he original topological space.
@en
Фактор-простір — простір класі ...... м відношенням еквівалентності.
@uk
位相空間論およびそれに関連する数学の各分野において、等化空間 ...... 空間から新たな空間を構成する方法の一つとして広く用いられる。
@ja
label
Espaço topológico quociente
@pt
Quotient space (topology)
@en
Quotiententopologie
@de
Quotiënttopologie
@nl
Topologia ilorazowa
@pl
Topologia quocient
@ca
Topologia quoziente
@it
Topologie quotient
@fr
Topología cociente
@es
Фактор-простір
@uk