pi-base
Regular extremally disconnected P-space of non-measurable size
Hello, since we already have all the tools for it in pi-base, I thought the following theorem would be a nice addition, which shows that modulo size, all regular extremally disconnected P-spaces are discrete.
The theorem is [ $T_3$ + extremally disconnected + P-space + non-measurable => discrete]
The above is an exercise in Gillman and Jerison, and I will provide proof if requested (though it might get a bit lengthy).
While we're at it the following would be nice to prove or disprove for a possible simplified statement: [ $T_2$ + extremally disconnected + P-space => regular]
I was experimenting with filtering the Issues by label and found this. It looks like this is still open as of today
π-Base, Search for t3 + Extremally disconnected + p-space + Non-measurable cardinality + ~discrete
