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Results tagged with topological-vector-spaces
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user 46855
A topological vector space is a vector space $V$ over a topological field $\mathbb{K}$ (typically $\mathbb{K}=\mathbb{R}$ or $\mathbb{K}=\mathbb{C}$), together with a topology on $V$ such that vector addition and scalar multiplication are both continuous. Hilbert spaces and Banach spaces are examples of topological vector spaces.
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Generic topology on a field
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You might find useful the two books of S.Warner [Topological fields; topological rings], and the book N.Shell, Topological fields and near valuation. In Chap. 3 (The lattice o …
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