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Is there an interesting example of an infinite dimensional Topological Vector Space whose topology was initially induced by something other than a norm or inner product and was latter found out to be a normed/inner product space?

Alek Fröhlich
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    Most Frechet spaces. – J. De Ro Jan 29 '22 at 22:27
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    @QuantumSpace are they normable? Or just metrizable? – Alek Fröhlich Jan 29 '22 at 23:01
  • I suspect not many, if any... I'd be interested to see an example otherwise! For me, the way topologies arise is almost entirely by specifying a structure, and either demonstrating some form of completeness (to demonstrate the appropriateness of that topology), or taking a completion. – paul garrett Jan 29 '22 at 23:43

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