Can anyone give me an example of a Topological Vector Space that is not metrizable? I know that the neighborhood base of $0$ needs to be incountable, and all I can construct then is no topological vector space because the algebraic operations (especially multiplication) aren't continous.
2026-03-27 04:15:27.1774584927
Topological Vector Space not induced by Metric
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Take for instance $\mathbb{R}^{\mathbb{R}}$ with the product topology or the weak topology on an infinite-dimensional Banach space. You will find more examples here.