Can someone explain how topological vector spaces are more general than normed ones. So this means that if I have a normed vector space, [tex]X[/tex], it would have to induce a topology. I was thinking the base for this topology would consist of sets of the form [tex]\{y\in X: ||x-y||<\epsilon, \textrm{for some x$x\in X$ and $\epsilon>0$}\}[/tex], which is the analogue of the open ball centred at y with radius epsilon. Is this correct?(adsbygoogle = window.adsbygoogle || []).push({});

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# Normed and topological vector spaces

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