Glasnik matematički, Vol. 44 No. 2, 2009.
Original scientific paper
https://doi.org/10.3336/gm.44.2.15
Metrization of pro-morphism sets
Nikica Uglešić
; University of Zadar, Pavlinovićeva bb, 23000 Zadar, Croatia
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.
Keywords
Pro-category; shape; quasi-equivalence; semi-stability; complete metric; compactum; FANR; ANR
Hrčak ID:
44059
URI
Publication date:
9.12.2009.
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