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Previously, in this post I've shown the following characterization of spaces with only zero-dimensional compactifications: Theorem. Let $X$ be strongly zero-dimensional and $\beta X\setminus X$ ...

Recently I've proven the following theorem Theorem. Let $X$ be a zero-dimensional locally compact Hausdorff space. Then the following are equivalent: Every compactification of $X$ is zero-dimensional....

I am looking for locally compact Hausdorff spaces $X$ with the following property: If $f:X\to Y$ is a perfect map onto locally compact Hausdorff space $Y$, then $Y$ is zero-dimensional. One can see ...