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Results tagged with banach-spaces
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user 80774
A Banach space is a complete normed vector space: A vector space equipped with a norm such that every Cauchy sequence converges.
11
votes
Accepted
Two vector spaces with homeomorphic open subsets are isomorphic?
This is false. All separable Banach spaces, for example, are homeomorphic.Indeed, there is a considerable body of work on when topological vector spaces are homeomorphic (see Bessaga and Pelczynski " …
- 196
7
votes
Existence of closed operators with arbitrary dense domain of a given Banach space
This cannot happen, if, e.g., $Y$ is a countable union of finite dimensional subspaces (by the Baire category theorem). Suitable examples are given by the spaces of finite sequences in $\ell^p$.
Ed …
- 196