Every topological vector space is completely regular. My question is, is the converse true? That is, is every completely regular topology induced by some topological vector space?
If not, does anyone know of a counterexample?
2026-03-25 08:07:56.1774426076
Is every completely regular topology induced by some topological vector space?
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Just in case the question was intended to be as @Aweygan suggested: Every completely regular space embeds into a power of the interval [0,1] with the product topology. (This is the main step in one construction of the Stone-Cech compactification.) So it embeds into a power of ℝ, which is a topological vector space.