On Countability and Separability of the Unbounded Norm Topology Generated by Ideals
Fahreezan Sheraz Diyaldin and Made Tantrawan

Universitas Gadjah Mada

Abstract

In the paper of Kandic and Vavpetic (2023), it has been proved that separability and second countability of the unbounded norm topology are equivalent. In this talk, we show that the equivalence may fail when the unbounded norm topology is replaced by the unbounded norm topology generated by some order ideals. Further, we provide a necessary and sufficient condition on when the equivalence holds for unbounded norm topology generated by an ideal of a norm lattice.

Keywords: unbounded norm topology, separability, second countability, norm lattices

Topic: Functional Analysis