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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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Can a topological vector space be probabilistic metric space too? [closed]

Is it possible to have probabilistic metric space (S,F,T) be a topological vector space too? In specific way, the probabilistic metric space is Menger and does not have a norm, however with Menger spa …
nastaran noorivatan's user avatar