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arXiv · 2105.03126

On separability of unbounded norm topology

Marko Kandić·Aleš Vavpetič
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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 $X$ over a semi-finite measure space is separable if and only if it has a $\sigma$-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.

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Marko Kandić, Aleš Vavpetič. 2021-05-07. On separability of unbounded norm topology. https://arxiv.org/abs/2105.03126

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