Timeline for A question about density character of Banach spaces.
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 6, 2011 at 20:56 | comment | added | Peter | Where can I find a reference about it? Or better, how do you prove that fact? (I mean, $Y\le X$ implies $dc(Y)\le dc(X)$)? | |
| Nov 5, 2011 at 14:01 | comment | added | Ramiro de la Vega | Peter $dc(\mathbb{I})=\aleph_0$ since it is in fact second countable. The claim says "any metric space" and "any subspace". | |
| Nov 5, 2011 at 13:38 | vote | accept | Peter | ||
| Nov 5, 2011 at 13:38 | vote | accept | Peter | ||
| Nov 5, 2011 at 13:38 | |||||
| Nov 4, 2011 at 20:00 | comment | added | Peter | Take $X:=\mathbb{R}$ and $Y:=\mathbb{I}$ with the usual metric. Notice that $dc(X)=\aleph_0$ and $dc(Y)=2^{\aleph_0}$. Does your claim hold if both $X$ and $Y$ are complete in the metric sense? | |
| Nov 3, 2011 at 21:28 | history | answered | Ramiro de la Vega | CC BY-SA 3.0 |