On separability of unbounded norm topology
Functional Analysis
2021-05-10 v1
Abstract
In this paper, we continue the investigation of topological properties of unbounded norm (un-)topology in normed lattices. We characterize separability and second countability of un-topology in terms of properties of the underlying normed lattice. We apply our results to prove that an order continuous Banach function space over a semi-finite measure space is separable if and only if it has a -finite carrier and is separable with respect to the topology of local convergence in measure. We also address the question when a normed lattice is a normal space with respect to the un-topology.
Keywords
Cite
@article{arxiv.2105.03126,
title = {On separability of unbounded norm topology},
author = {Marko Kandić and Aleš Vavpetič},
journal= {arXiv preprint arXiv:2105.03126},
year = {2021}
}