Glasnik Matematicki, Vol. 44, No.2 (2009), 499-531.

METRIZATION OF PRO-MORPHISM SETS

Nikica Uglešić

Abstract.   Every pair of inverse systems X, Y in a category A, where Y is cofinite, admits a complete (ultra)metric structure on the set pro-A(X,Y). The corresponding hom-bifunctor is not, generally, an internal Hom. However, there exists a subcategory of pro-A, containing tow-A, for which the hom-bifunctor is an invariant Hom into the category of complete metric spaces. Application to the sets tow-HcANR(X,Y) yields several new interesting results concerning Borsuk's quasi-equivalence.

2000 Mathematics Subject Classification.   55P55, 54E50.

Key words and phrases.   Pro-category, shape, quasi-equivalence, semi-stability, complete metric, compactum, FANR, ANR.

DOI: 10.3336/gm.44.2.15

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