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.