Category:Normed Vector Space is Finite Dimensional iff Unit Sphere is Compact
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This category contains pages concerning Normed Vector Space is Finite Dimensional iff Unit Sphere is Compact:
Let $X$ be a normed vector space.
Let $\Bbb S = \map {\Bbb S_1} 0$ be the unit sphere centred at $0$ in $X$.
Then $X$ is finite dimensional if and only if $\Bbb S$ is compact.
Pages in category "Normed Vector Space is Finite Dimensional iff Unit Sphere is Compact"
The following 3 pages are in this category, out of 3 total.