Patrick Rabau

Results 311 comments of Patrick Rabau

Add the property Ordinal space and remove some redundant files

T497 is redundant. We already know ordinal spaces are LOTS and scattered by the other theorems. Hence totally disconnected. And totally disconnected LOTS are zero-dimensional. More comments later.

Add the property Ordinal space and remove some redundant files

(T490) [ordinal ==> locally relatively compact]: Among the various variants of locally compact properties, a strong combination is [weakly locally compact + regular] (= condition (4) in https://en.wikipedia.org/wiki/Locally_compact_space). It is...

Add the property Ordinal space and remove some redundant files

(T495) [ordinal + perfectly normal ==> countable]: The argument seems fine, but maybe a little too much for the justification without a reference. (The "General Reference Chart" does not really...

Add the property Ordinal space and remove some redundant files

T490: Let me try to explain what my reasoning was. Ordinal spaces are - weakly locally compact (WLC) (P23) - locally compact (P130) - locally relatively compact (P24) WLC is...

Add the property Ordinal space and remove some redundant files

(T496) [ordinal + ccc ==> countable]: This seems redundant by T495 combined with [LOTS + ccc ==> perfectly normal] (see https://topology.pi-base.org/spaces?q=lots%2Bccc%2B%7EPerfectly+normal).

Add the property Ordinal space and remove some redundant files

Nice cleanup of the redundant traits. Just one file S35|P31 should not have been removed.

The property "cannot be written as a countable disjoint union of closed subsets with at least two being nonempty"

Yeah, it seems it would be interesting to add the property, as there are various results in the literature mentioning it, even if not with a special name. @Jianing-Song We...

The property "cannot be written as a countable disjoint union of closed subsets with at least two being nonempty"

Sorry, it seems I misrepresented what I wanted to say. I was just noting that spaces that are finite and connected would match the definition of the new property. And...

The property "cannot be written as a countable disjoint union of closed subsets with at least two being nonempty"

> Thanks! Yes I am new to github, so I have never done a pull request before, but I would be happy to learn to make one. Awesome! What I...

The property "cannot be written as a countable disjoint union of closed subsets with at least two being nonempty"

> Just another thing: In the Math Stack Exchange question cited above (https://math.stackexchange.com/q/6314) it is stated that ... can be found in General Topology by Ryszard Engelking (Thm 6.1.27). Could...