Fréchet space
(Q1471397)
locally convex space that is complete with respect to a translation-invariant metric
locally convex space that is complete with respect to a translation-invariant metric
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Current Data About
Fréchet space
| (P31) |
(Q24034552)
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| (P138) |
(Q22662)
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| (P279) |
(Q4442333)
(Q3554820) (Q2664426) (Q158565) (Q1317594) (Q1150180) |
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| (P1889) |
(Q2740469)
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| (P2534) |
\begin{aligned}&\|-\|_1,\|-\|_2,\dotsc\colon X\to\mathbb R_{\ge0}\\&\|\lambda x\|_k=|\lambda|\|x\|_k\\&\|x+y\|_k\le\|x\|_k+\|y\|_k\\&x=0\iff\forall k>0\colon\|x\|_k=0\\&U\in\operatorname{Open}(X)\iff\forall u\in U\exists K>0,r>0\colon\{x\in X\colon\forall k\ge K\colon\|u-x\|_k<r\}\subset U\end{aligned}
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| (P6104) |
(Q8487137)
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other details
| aliases |
Frechet space |
| description | locally convex space that is complete with respect to a translation-invariant metric |
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