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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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Deleting "weak homeomorphism" in a Hilbert space

It is well-known that there exists a homeomorphism $h$ from an infinite-dimensional Hilbert space $H$ to $H\setminus\{0\}$. Does there exist a "weak homeomorphism" $g:H \to H\setminus\{0\}$, that is, …