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On Banach spaces of regulated functions

Drewnowski L.

Commentationes Mathematicae

2017

Vol 57, No. 2

153--169

For a relatively compact subset S of the real line R, let R(S) denote the Banach space (under the sup norm) of all regulated scalar functions defined on S. The purpose of this paper is to study those closed subspaces of R(S) that consist of functions that are left-continuous, right-continuous, continuous, and have a (two-sided) limit at each point of some specified disjoint subsets of S. In particular, some of these spaces are represented as C(K) spaces for suitable, explicitly constructed, compact spaces K.