Timeline for Examples of non-metrizable spaces
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 27, 2014 at 6:24 | comment | added | barcelos | Oddly, this false statement seems to have stood the test of time. The space of tempered distributions is NOT metric although, being a Silva space, i.e. an inductive limit of a sequence of Banach spaces with compact intertwining maps it shares many of their properties (see, e.g., Köthe, "Topological linear spaces". Functional analysis abounds in important non-metrisable spaces, in distrubtion theory as mentioned above, but also in measure theory. | |
| Jan 14, 2011 at 22:10 | vote | accept | Sudip Paul | ||
| Jan 14, 2011 at 22:09 | vote | accept | Sudip Paul | ||
| Jan 14, 2011 at 22:10 | |||||
| Jan 14, 2011 at 7:24 | comment | added | Pietro Majer | The pre-dual, that is the space $\mathcal{D}(\Omega)$ of $C^\infty$ compactly supported functions on $\Omega$, is already non-metrizable (it is a countable union of closed linear subspaces, namely, the subspaces of functions with supports in given compact sets. It is sequentially complete, so it can't be metrizable by Baire theorem). Yet it shares several properties of metric spaces, since it is an inductive limit of Fréchet spaces; which is the reason why sequences suffice. | |
| Jan 14, 2011 at 7:16 | history | edited | Chris Eagle | CC BY-SA 2.5 |
rm now-superfluous note
|
| Jan 14, 2011 at 7:13 | history | edited | Pietro Majer | CC BY-SA 2.5 |
added 1 characters in body
|
| Jan 14, 2011 at 7:02 | history | answered | Zen Harper | CC BY-SA 2.5 |