Timeline for Importance of separability vs. second-countability
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 19, 2013 at 6:08 | comment | added | Nik Weaver | It sounds like you are asking why separability is important. Speaking from my area of expertise, I could tell you any number of basic theorems about separable C*-algebras which fail in the nonseparable case. | |
| May 19, 2013 at 3:53 | comment | added | Martin | No, I was asking an honest question. I agree that it is a useful fact, but it seems more related to continuity than separability per se: It is a characteristic property of continuous functions that the image of the closure is contained in the closure of the image. Thus, dense sets are mapped to dense sets. What makes the instantiation of this observation to countable dense sets particularly noteworthy and important? | |
| May 18, 2013 at 20:50 | comment | added | Nik Weaver | @Martin: do you wish to tell me that this simple fact is not important? | |
| May 18, 2013 at 19:50 | comment | added | The User | @Martin That was indeed not that kind of theorems I was looking for (a property does not get important by being well-behaved when taking images). But I think it is worth mentioning (I have also mentioned it in my question). | |
| May 18, 2013 at 19:31 | comment | added | Martin | What makes the simple fact that images of separable spaces are separable an important theorem? | |
| May 18, 2013 at 18:13 | history | answered | Nik Weaver | CC BY-SA 3.0 |