# Onto monotone map of an interval is an arc

## Theorem

If $X$ is a nondegenerate Hausdorff topological space and $f \colon [0,1] \rightarrow X$ is a monotone map onto $X$, then $X$ is an arc.

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If $X$ is a nondegenerate Hausdorff topological space and $f \colon [0,1] \rightarrow X$ is a monotone map onto $X$, then $X$ is an arc.

- This page was last edited on 23 September 2016, at 17:27.