论文标题
使用Zorn的引理从路径上构建弧线
Constructing arcs from paths using Zorn's Lemma
论文作者
论文摘要
众所周知的事实是，每个路径连接的Hausdorff空间都是弧形连接的。通常，这一结果被视为连续理论一系列相当技术结果的结果。在本说明中，我们展示了此陈述的直接而简单的证明，该证明明确地使用了Zorn的引理。此外，通过仔细分解证明，我们确定了与代数拓扑相关的一类空间的适度改进。
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.
