Spaces of functions with countably many discontinuities

2006/12/12 by Richard Haydon, R Haydon, Haydon, R +6
Mathematics · #46B03 #54H05 #Advanced Banach Space Theory #Advanced Topology and Set Theory #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #General Topology (math.GN) #math.FA #math.GN #msc:46B03 #msc:54H05

paper · pdf · doi:10.48550/arxiv.math/0612307

arxiv created 2006/12/12 · openalex publication_date 2006/12/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Γ be a Polish space and let K be a separable and pointwise compact set of real-valued functions on Γ. It is shown that if each function in K has only countably many discontinuities then C(K) may be equipped with a T_p-lower semicontinuous and locally uniformly convex norm, equivalent to the supremum norm.

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