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A Hilbert space $H$ is a real or complex vector space endowed with an inner product such that $H$ is a complete metric space when endowed with the norm induced by this inner product.

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Variation of concept of a Lusin space

Citing from Wikipedia, A Hausdorff topological space is a Lusin space if some stronger topology makes it into a Polish space. Is there a (previously studied) analogous concept of a Hausdorff (locall …