Spaces of functions with countably many discontinuities
Functional Analysis
2007-05-23 v1 General Topology
Abstract
Let be a Polish space and let be a separable and pointwise compact set of real-valued functions on . It is shown that if each function in has only countably many discontinuities then may be equipped with a -lower semicontinuous and locally uniformly convex norm, equivalent to the supremum norm.
Cite
@article{arxiv.math/0612307,
title = {Spaces of functions with countably many discontinuities},
author = {R Haydon and A Molto and J Orihuela},
journal= {arXiv preprint arXiv:math/0612307},
year = {2007}
}