If one has a map $f$ from a topological space $X$ to another space $Y$ and then one takes the compactification of $Y$ (for example, if $Y = \mathbb{R}^n$ the compactification is constructed by taking the point at infinity), does $f^{-1} $ take a point in the compactification of $Y$ back to a point in the compactification of $X$?
2026-03-26 17:51:32.1774547492
Map from Compactification to Original Space
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