English

A really simple elementary proof of the uniform boundedness theorem

Functional Analysis 2011-05-03 v2

Abstract

I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.

Keywords

Cite

@article{arxiv.1005.1585,
  title  = {A really simple elementary proof of the uniform boundedness theorem},
  author = {Alan D. Sokal},
  journal= {arXiv preprint arXiv:1005.1585},
  year   = {2011}
}

Comments

LaTex2e, 5 pages. Version 2 improves the exposition by isolating the key lemma. To appear in the American Mathematical Monthly

R2 v1 2026-06-21T15:20:40.396Z