Timeline for LCH spaces $X$ such that if $Y$ is a perfect image of $X$, then $Y$ is zero-dimensional
Current License: CC BY-SA 4.0
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| Nov 10 at 17:33 | comment | added | Jakobian | Thank you, inspired by this answer I've shown that for any locally compact Hausdorff scattered space $Y$ there exists a space $X$ with only zero-dimensional compactifications and $\beta X\setminus X\cong Y$. Moreover, whenever $X$ is a strongly zero-dimensional space and $\beta X\setminus X$ is locally compact, then having only zero-dimensional compactifiactions is equivalent to $\beta X\setminus X$ being scattered. | |
| Nov 9 at 19:09 | vote | accept | Jakobian | ||
| Nov 9 at 15:26 | history | answered | KP Hart | CC BY-SA 4.0 |