Timeline for Name for topological spaces where "every point has a local base wellordered by reverse inclusion"?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 3, 2023 at 5:37 | comment | added | PatrickR | See also mathoverflow.net/questions/202280. | |
| Feb 1, 2019 at 14:39 | comment | added | Cla | Thank you for the references. Those together with the answer below I think are enough to close the question. | |
| Feb 1, 2019 at 14:28 | vote | accept | Cla | ||
| Feb 1, 2019 at 14:21 | answer | added | Ramiro de la Vega | timeline score: 13 | |
| Jan 31, 2019 at 20:38 | comment | added | Clemens Sämann | Ah, sorry! I thought I checked what is meant but I mixed it up after all. Sure I let it stand as it is. | |
| Jan 31, 2019 at 20:27 | comment | added | Robert Furber | @ClemensSämann That would be if the neighbourhoods were well-ordered by inclusion. Cla asks for neighbourhood bases well-ordered by reverse inclusion. For instance, any metric space is an example, because we can use balls of radius $\frac{1}{n}$ for $n$ a positive natural number. Please don't delete your comment, as others may have the same confusion. | |
| Jan 31, 2019 at 20:06 | comment | added | Clemens Sämann | If by well-ordered you really mean en.wikipedia.org/wiki/Well-order, then this implies that every point has a minimal neighborhood. Such spaces are called "Alexandroff spaces" (not to be confused with Alexandrov spaces, i.e. of metric spaces with curvature bounds). See emis.de/journals/AMUC/_vol-68/_no_1/_arenas/arenas.pdf: Arenas, F.G.. "Alexandroff spaces.." Acta Mathematica Universitatis Comenianae. New Series 68.1 (1999): 17-25 and he refers to Alexandroff P.,Diskrete Räume, Mat.Sb.(N.S.)2(1937),501–518, for the first study of such spaces. | |
| Jan 31, 2019 at 19:03 | comment | added | Martin Sleziak | Horst Herrlich has shown in Quotienten geordneter Räume und Folgenkonvergenz that pseudoradial spaces are exactly quotients of the spaces you describe. | |
| Jan 31, 2019 at 18:33 | comment | added | Will Brian | My friend Robert Leek has done some work that includes looking at spaces with this property. I don't know how standard his terminology is, but he refers to them as "well-based spaces" (see Definition 2.1 in arxiv.org/pdf/1401.6519.pdf). | |
| Jan 31, 2019 at 18:23 | history | edited | Cla | CC BY-SA 4.0 |
added 98 characters in body
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| Jan 31, 2019 at 18:11 | history | asked | Cla | CC BY-SA 4.0 |