Universally uniformly continuous metric spaces
General Topology
2018-01-03 v2
Abstract
We answer the question: "on which metric spaces are all continuous functions uniformly continuous?" Our characterization theorem improves and generalizes a previous result due to Levine and Saunders, and in particular is applicable to metric spaces which are "infinite dimensional."
Keywords
Cite
@article{arxiv.1712.09160,
title = {Universally uniformly continuous metric spaces},
author = {Katrina Gensterblum and Peikai Qi and Willie Wong},
journal= {arXiv preprint arXiv:1712.09160},
year = {2018}
}
Comments
Fall 2017 undergraduate research project for the first and second named authors. After posting to arXiv, it was brought to our attention that the results proven herein are not new; we thank Subiman Kundu for this information, which we also acknowledged in V2 of this posting