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.
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.
