Timeline for Why the name 'regular' space?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 27, 2021 at 8:33 | comment | added | reliquia | For the historical record, the concept of regularity was introduced by the Austrian mathematician L. Vietoris (1921) under name of Axiom (E) (his previous axioms were those of Hausdorff for what we now call a $T_2$-space). In the same remarkable paper which was written while Vietoris was in service during and a POW in Italy afer WWI (readily available on-line), he introduced the concepts of filter bases, nets and their convergence, their use in the definition of compactness and, tacitly, $T_4$-spaces (he showed that compact spaces have this property). Ref. „Stetige Mengen“ in Monatsheft. | |
| May 24, 2021 at 15:21 | comment | added | Andreas Blass | Some people, like the OP, define "regular" to imply $T_1$, while $T_3$ doesn't. Others, like @WlodAA use the opposite convention. Corollary 1: If you work with non-$T_1$ topologies like the Zariski topology, don't use either version of "regular". Corollary 2: Algebraic geometers can redefine "regular" to mean something totally different. | |
| May 24, 2021 at 9:44 | comment | added | Carl-Fredrik Nyberg Brodda | This all reminds me of an old joke by J.-P. Serre: "regular" is a well-defined notion in mathematics -- it is so well-defined that it has about 23 different definitions. | |
| May 24, 2021 at 8:56 | comment | added | Pietro Majer | @WlodAA If I'm not wrong, "regular" was introduced as a religious term, "member of a religious order", thus following the "regula" of the order. Isn't imaginative enough, associating a $T_3$ topological space with the calm quiet regular life in a monastery :) ? | |
| May 24, 2021 at 8:47 | comment | added | Pietro Majer | It is true that "regular" is a generic and somehow overused adjective , which may be a bit unsatisfactory (yet definitely better than funny or creative names!). But I'd say there is something more than just "following/within a rule". "Regular" usually refers to some smoothness or continuity (recall that the etymology is from "regula", "ruler"); in this sense the name fits quite well with the separation property. | |
| May 24, 2021 at 7:12 | comment | added | Wlod AA | "Regular" is just another lazy and unimaginative name. | |
| May 24, 2021 at 7:10 | comment | added | Wlod AA | Condition 2 alone stands for "regular". Conditions 1+2 stands for $\ T_3.$ | |
| May 24, 2021 at 7:02 | comment | added | Nate Eldredge | It's just one of those generic overused adjectives that has no real meaning except "having some desirable property". Likewise normal, perfect, proper, admissible, etc. | |
| May 24, 2021 at 6:46 | comment | added | Anthony Quas | I don't think it's a very descriptive name. Regular means "following the rule" or standard. Clearly one of the first spaces point set topologists were considering was the real line. So it would be reasonably natural to call spaces with some properties of the real line "regular", leaving the "irregular" spaces with unusual properties. A related word in English that is similarly overused is normal. | |
| May 24, 2021 at 6:22 | history | asked | mahdi meisami | CC BY-SA 4.0 |