Increasing, nondecreasing, and virtually continuous functions (Q2731275)

Problems concerning the continuity of real-valued functions have been recurring themes in constructive mathematics. The relationships between pointwise continuity, uniform continuity, monotonicity, and extendibility have proven difficult to unravel. As is usual, the relatively few classical concepts have been divided and subdivided into a goodly number of related concepts. This has been required because over-simplifying classical principles, such as the (ital) excluded middle (end ital), are not available to conjoin constructively distinct notions. This paper contributes to the study of the extendibility of certain increasing functions, defined on a dense subset of an interval, and satisfying certain continuity conditions. The methods used are typical of constructive analysis as promoted by Errett Bishop.