Talk:Strongly Locally Compact Space is Weakly Locally Compact

I would be happy to see Maloney's work to be revisited, perhaps as a separate page: Strongly Locally Compact Hausdorff Space is Locally Compact.

I have been reminded about the "alternative definition" of Definition:Locally Compact Space and reckon we ought to take another look at everywhere "locally compact" has been used. I understand that the "alternative definition" is now considered to be wrong. Its initial conception was in the context of Hausdorff spaces, which at one time was the only sort of spaces being investigated. Hence it was taken for granted that the alternative definition was appropriate.

However, the new definition is wider than the old: non-Hausdorff spaces may be Definition:Locally Compact Space without necessarily being Definition:Locally Compact Space.

So my plan is to coin a new name Definition:Locally Compact by Neighborhood for the alternative definition. This then of course opens up another category of compactness. Care of course needs to be taken to ensure that when a source work uses "locally compact", we use the version they are referring to.

This work is on my todo list, I just need to take a run-up. --prime mover (talk) 18:24, 6 June 2015 (UTC)


 * Meh. There is also a problem with Definition:Strongly Locally Compact Space because it is actually now *weaker* than the new Definition:Locally Compact Space. So we ought to make sure that everything remains coherent, probably by inserting suitable remarks. &mdash; Lord_Farin (talk) 21:36, 6 June 2015 (UTC)