Constructing arcs from paths using Zorn's Lemma
General Topology
2025-01-27 v1
Abstract
It is a well-known fact that every path-connected Hausdorff space is arcwise connected. Typically, this result is viewed as a consequence of a sequence of fairly technical results from continuum theory. In this note, we exhibit a direct and simple proof of this statement, which makes explicit use of Zorn's Lemma. Additionally, by carefully breaking down the proof, we identify a modest improvement to a class of spaces relevant to algebraic topology.
Cite
@article{arxiv.2207.07242,
title = {Constructing arcs from paths using Zorn's Lemma},
author = {Jeremy Brazas},
journal= {arXiv preprint arXiv:2207.07242},
year = {2025}
}
Comments
Expository Article. 7 pages, 2 figures