When:
August 18, 2020 @ 6:00 am – 8:00 am
2020-08-18T06:00:00-10:00
2020-08-18T08:00:00-10:00
Where:
Lecture held in Elysium

Title: Group dualities: G-barrelled groups
A natural notion in the framework of abelian groups are the group dualities. The most efficient definition of a group duality is simply a pair $(G, H)$, where $G$ denotes an abstract abelian group and $H$ a subgroup of characters of $G$, that is $H leq {rm Hom}(G, mathbb T)$. Two group topologies for $G$ and $H$ appear from scratch in a group duality $(G, H)$: the weak topologies $sigma(G, H)$ and $sigma (H, G)$ respectively. Are there more group topologies either in $G$ or $H$ that can be strictly related with the duality $(G, H)$? In this sense we shall define the term “compatible topology” and loosely speaking we consider the compatible topologies as members of the duality.
The same question for a metrizable, or a $k$-group topology.
We shall also introduce the $g$-barrelled groups, a class for which the Mackey-Arens Theorem admits an optimal counterpart. We study also the existence of $g$-barrelled topologies in a group duality $(G, H)$.