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