Sequences of real functions on [0,1] in constructive reverse mathematics (Q1001912)

The paper deals with (uniformly) continuous functions and with (uniform) equicontinuity, (uniform) convergence, and totally boundedness of sequences of functions. The functions are real-valued and defined on the unit interval, on the Cantor space, respectively. The investigation is carried out from various perspectives: Bishop-style constructive mathematics, classical mathematics, intuitionistic mathematics, and constructive recursive mathematics. Besides an overview over the current state of research in this specific area, the paper also contains new results in terms of constructive reverse mathematics. People working on constructive mathematics or, more generally, on foundations of analysis, will find this paper interesting.