What is an example of a connected Hausdorff space $X$ with $|X|>1$ and a surjective continous map $f:X\to (X\times X)$?



Example of connected Hausdorff space $X$ and surjective continous map $f:X\to X\times X$
$X=[0,1]$. See [Space-filling curve.](https://en.wikipedia.org/wiki/Space-filling_curve)


