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arXiv · 2207.07242

Constructing arcs from paths using Zorn's Lemma

Jeremy Brazas
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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.

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Jeremy Brazas. 2022-07-15. Constructing arcs from paths using Zorn's Lemma. https://doi.org/10.1216/rmj.2024.54.965

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