Abstract
Some properties of \({\mathcal E}\)-continuous functions are investigated. In particular, the maximal family with respect to outer and inner compositions for the family of all \({\mathcal E}\)-continuous functions are described. Moreover, under some assumptions on \({\mathcal E}\) it is proved that every function \(f:\mathbb{R} \rightarrow \mathbb{R} \) can be represented as the composition of two \({\mathcal E}\)-continuous function. Similarly, every function \(f:\mathbb{R} \rightarrow \mathbb{R} \) can be represented as the limit of a transfinite sequence of \({\mathcal E}\)-continuous functions.
Citation
Krzysztof Banaszewski. "On ℰ-continuous functions." Real Anal. Exchange 21 (1) 203 - 215, 1995/1996.
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