Saturday, 5 April 2008

gn.general topology - Minimal Hausdorff

A Hausdorff space (X,tau) is said to be minimal Hausdorff if for each topology tausubseteqtau with tauneqtau 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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