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Sep 22, 2015 at 16:42 comment added Taras Banakh In case of a Cantor set $X$ for the space $Y$ we can take any closed subset containing more than one point. If $X$ is the space of rationals, then for $Y$ we can take any non-compact $G_\delta$-subset of $Y$. This means that in case of zero-dimensional spaces we have a lot of freedom.
Sep 9, 2015 at 19:49 history asked Daron CC BY-SA 3.0