Path-Connected Hausdorff Space is Arc-Connected

Theorem

Let $T = \struct {S, \tau}$ be a Hausdorff ($T_2$) topological space which is path-connected.

Then $T$ is arc-connected.


Proof


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Sources

  • 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): arc-connected
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