Spaces of functions with countably many discontinuities

Details Spaces of functions with countably many discontinuities Spaces of functions with countably many discontinuities

2006-12-12

arxiv.org/abs/math/0612307v1

Mathematics

Functional Analysis

Scientific paper

Let $\Gamma$ be a Polish space and let $K$ be a separable and pointwise
compact set of real-valued functions on $\Gamma$. 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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