Constructing arcs from paths using Zorn's Lemma
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912201554526208 |
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| author | Brazas, Jeremy |
| author_facet | Brazas, Jeremy |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_07242 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Constructing arcs from paths using Zorn's Lemma Brazas, Jeremy General Topology 54C10, 54C25, 54B30 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. |
| title | Constructing arcs from paths using Zorn's Lemma |
| topic | General Topology 54C10, 54C25, 54B30 |
| url | https://arxiv.org/abs/2207.07242 |