Compactness in constructive analysis revisited.

Christoph Kreitz, Klaus Weihrauch.

Annals of pure and applied logic, 36:29--38, 1987.


Abstract

In two previous papers we have presented a unified Type 2 theory of computability and continuity and a theory of representations. In a third one representations useful for a new kind of constructive analysis were presented. As an application of these concepts we consider constructive compactness. We introduce `reasonable' representations of closed and compact sets and prove two different versions of the Heine-Borel theorem. Theorems concerning functions continuous on compact sets are investigated relative to constructivity properties and it is shown that usually topological properties (i.e., discontinuity) are the true reasons for nonconstructivity.


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Bibtex Entry

@Article{ar:KreitzWeihrauch87a, author = "Christoph Kreitz and Klaus Weihrauch", title = "Compactness in constructive analysis revisited", journal = "Annals of pure and applied logic", volume = 36, year = 1987, pages = "29-38" }