F. Riesz's theorem

It has been suggested that this article be merged into Riesz's lemma. (Discuss) Proposed since July 2024.

F. Riesz's theorem (named after Frigyes Riesz) is an important theorem in functional analysis that states that a Hausdorff topological vector space (TVS) is finite-dimensional if and only if it is locally compact. The theorem and its consequences are used ubiquitously in functional analysis, often used without being explicitly mentioned.