Compactness in constructive analysis revisited (Q1100202)

This paper, which follows other papers of the same authors, deals with constructive compactness. Representations of closed and compact subset of \({\mathbb{R}}\) are introduced and two different versions of the Heine-Borel theorem are proved. It is pointed out the fundamental role of topology in constructive analysis, and in particular of discontinuity as the main reason for nonconstructivity.