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Homogeneous spaces with a cut point are T_1. #942

Open Almanzoris opened 4 days ago

Almanzoris commented 4 days ago

T209 could be referenced.

I'm going to reword the second either ... or ...; if the cut point is open, it would be reached that it is closed aswell.

GeoffreySangston commented 3 days ago

Depending on what everyone decides to do with Issue https://github.com/pi-base/data/issues/940, a theorem involving that property (currently number 3 on the list) could be referenced. Edit: Or maybe this one gets deduced automatically?

Almanzoris commented 3 days ago

Good point! I hadn't read this... I could close it or change it to Homogeneous + Has a closed point ==> $T_1$, which would be the number 6 in the list. But, I wouldn't mind closing it, knowing that you have opened the issue before me making the PR. You probably have proven it already.

GeoffreySangston commented 3 days ago

Maybe don't close it until that issue gets resolved. If you have the time, maybe you could weigh in any thoughts you have on that issue?

Almanzoris commented 3 days ago

Alright! I will read it better later today. I already agree with adding the property "Has a closed point".

GeoffreySangston commented 3 days ago

I already agree with adding the property "Has a closed point".

Oh sorry I didn't notice you did!

david20000813 commented 1 day ago

This will indeed get automatically deduced if has a closed point and the theorems referenced in #940 is added. Indeed, combining theorems 3 and 6 in #940, and https://topology.pi-base.org/spaces?q=Homogeneous+%2B+Has+a+cut+point+%2B+Has+an+isolated+point gives the result.

Almanzoris commented 1 day ago

Yeah, I just missed the issue.