F-space
In functional analysis, an F-space is a vector space V over the real or complex numbers together with a metric d : V × V → ℝ so that 1.
* Scalar multiplication in V is continuous with respect to d and the standard metric on ℝ or ℂ. 2.
* Addition in V is continuous with respect to d. 3.
* The metric is translation-invariant; i.e., d(x + a, y + a) = d(x, y) for all x, y and a in V. 4.
* The metric space (V, d) is complete.
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F-space
In functional analysis, an F-space is a vector space V over the real or complex numbers together with a metric d : V × V → ℝ so that 1.
* Scalar multiplication in V is continuous with respect to d and the standard metric on ℝ or ℂ. 2.
* Addition in V is continuous with respect to d. 3.
* The metric is translation-invariant; i.e., d(x + a, y + a) = d(x, y) for all x, y and a in V. 4.
* The metric space (V, d) is complete.
has abstract
Em matemática, uma espaço veto ...... spaço de Banach é um F-espaço.
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In de functionaalanalyse, een ...... alisaties van fréchet-ruimten.
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In functional analysis, an F-s ...... atisfies the above properties.
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В математике, линейное метриче ...... еским векторным пространством.
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У математиці, лінійний метричн ...... ологічним векторним простором.
@uk
関数解析学における F-空間（Fくうかん、英語: F-spa ...... 質を満足する仕方で距離化可能であることを要求するのみである。
@ja
함수해석학에서, F-공간은 다음을 만족하는 실수또는 복 ...... 만족시키는 방법으로 거리화 가능 할 것을 필요로 한다.
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1,021,876,133
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math statement
Let be any metric on a vector ...... space then is a complete-TVS.
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Theorem
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note
Klee
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Em matemática, uma espaço veto ...... spaço de Banach é um F-espaço.
@pt
In de functionaalanalyse, een ...... alisaties van fréchet-ruimten.
@nl
In functional analysis, an F-s ...... tric space (V, d) is complete.
@en
В математике, линейное метриче ...... ально выпуклые F-пространства.
@ru
У математиці, лінійний метричн ...... ологічним векторним простором.
@uk
関数解析学における F-空間（Fくうかん、英語: F-spa ...... 質を満足する仕方で距離化可能であることを要求するのみである。
@ja
함수해석학에서, F-공간은 다음을 만족하는 실수또는 복 ...... 만족시키는 방법으로 거리화 가능 할 것을 필요로 한다.
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F-espaço
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F-ruimte
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F-space
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F-пространство
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F-простір
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F-空間
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F-공간
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