Timeline for Properties of the weak-$*$ topology
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Jul 30, 2013 at 23:39 | comment | added | Johannes Hahn | Regarding the definition: In the world of valued fields the notion of an absolutely convex set still makes sense. $A\subseteq V$ is absolutely convex if $|\mu|+|\lambda|\leq 1 \implies \forall a,b\in A: \lambda a+ \mu b \in A$. Now the set $\lbrace\lambda\in K : |\lambda|\leq 1\rbrace$ is just the valuation ring $\mathcal{O}$ of the valued field $K$ and an absolutely convex subset is nothing else then an $\mathcal{O}$-submodule of $V$. Therefore we can just apply the definition "there is a neighborhood base of the origin consisting of absolutly convex subsets of V". | |
| Jul 30, 2013 at 23:37 | comment | added | Johannes Hahn | In fact it is locally convex for $\mathbb{C}$ and $\mathbb{Q}_p$ as well with the same proof. | |
| Jul 30, 2013 at 21:46 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jul 30, 2013 at 18:15 | history | answered | Gerald Edgar | CC BY-SA 3.0 |