Compactness in constructive analysis revisited.


Christoph Kreitz, Klaus Weihrauch.  
Annals of pure and applied logic, 36:2938, 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 HeineBorel
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 = "2938" } 