Original scientific paper

Ultrametrization of pro*-morphism sets

Nikica Uglešić ; University of Zadar, Zadar, Croatia

Abstract

For every pair of inverse systems $\boldsymbol{X}$, $\boldsymbol{Y}$ in a category $\mathcal{A}$, where $\boldsymbol{Y}$ is cofinite, there exists a complete ultrametric structure on the set $pro^{\ast }\mbox{-}\mathcal{A}(\boldsymbol{X},\boldsymbol{Y})$. The corresponding hom-bifunctor is the internal and invariant $Hom$ of a subcategory, containing $tow^{\ast }\mbox{-}\mathcal{A}$, in the category of complete metric spaces. Several applications to the shapes (ordinary, coarse and weak) are considered.

Keywords

pro-category; pro*-category; complete ultrametric; shape; coarse shape; weak shape; quasi-equivalence; semi-stability; compactum; polyhedron; ANR

Hrčak ID:

101382

URI

https://hrcak.srce.hr/101382

Publication date:

10.5.2013.

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