A Hausdorff space (X,tau) is said to be minimal Hausdorff if for each topology tau′subseteqtau with tau′neqtau the space (X,tau′) is not Hausdorff.
Every compact Hausdorff space is minimal Hausdorff.
I would like to know:
1) Is every minimal Hausdorff space compact?
2) Does every Hausdorff topology contain a minimal Hausdorff topology?
Many thanks!
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