Timeline for Cardinality of $C^*([0,1])$
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 26, 2014 at 8:44 | vote | accept | pre-kidney | ||
| Jul 23, 2014 at 8:21 | comment | added | blackburne | Sorry, the probability measures on $[0,1]$, being compact, are homeomorphic to the Hilbert cube. | |
| Jul 23, 2014 at 8:18 | comment | added | blackburne | This is an impeccable answer using appropriate set-theoretical techniques but it might be of interest to vlv that much more precise formulations are available in the context of descriptive topology in the sense that a very large class of polish spaces are not only of equal cardinality but even homeomorphic. Thus all separable Fréchet spaces (infinite dimensional, of course) and the space of probability measures on, say, $[0,1]$ are homeomorphic to a countable product of the reals. | |
| Jul 23, 2014 at 6:39 | history | answered | Joonas Ilmavirta | CC BY-SA 3.0 |