Transfinite dimensions
General Mathematics
2020-10-06 v1
Abstract
Let H be a Hilbert space and let F be the family of all countable subsets of an orthonormal basis of H. We show that if F is infinite then F is equipollent with every linear basis of the vector space H. In doing so we also present a short proof of the Erd\"os-Kaplansky theorem more natural and much easier than the one by Bourbaki.
Cite
@article{arxiv.2010.01983,
title = {Transfinite dimensions},
author = {Gerald Kuba},
journal= {arXiv preprint arXiv:2010.01983},
year = {2020}
}