2021/05/07 by Kandić, Marko, Vavpetič, Aleš
#46E30 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 46B42 #Secondary: 46A40
paper · doi:10.48550/arxiv.2105.03126
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 X over a semi-finite measure space is separable if and only if it has a σ-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.