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Spaces with every compactification $0$-dimensional which aren't locally compact
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....
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2
votes
1
answer
103
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LCH spaces $X$ such that if $Y$ is a perfect image of $X$, then $Y$ 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 ...
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