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Results tagged with topological-vector-spaces
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user 20733
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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Independence of the axiomatics of metric cones
A metric cone $C$ is a nonempty metric space (whose distance is denoted $d$) together with a map $\cdot\colon \mathbf{R}\times C \mapsto C$ satisfying these axioms:
$a\cdot(b\cdot x) = (ab)\cdot x$ …
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