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We prove that a continuum is an arc if and only if it contains exactly two non-cut points. We also prove that a continuum X is a simple closed curve if and only if for every pair of distinct points \(x,y\in X\) , \(X\setminus \{x,y\}\) is disconnected.

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Characterizing Arcs and Circles

  • 章节

  • 发表日期：

    2025年

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  • Alejandro Illanes

摘要

We prove that a continuum is an arc if and only if it contains exactly two non-cut points. We also prove that a continuum X is a simple closed curve if and only if for every pair of distinct points \(x,y\in X\) , \(X\setminus \{x,y\}\) is disconnected.