engleski

Metrization of pro-morphism sets

Every pair of inverse systems <b>X</b>, <b>Y</b> in a category <font face="Brush Script MT, Script, Times New Roman">A</font>, where <b>Y</b> is cofinite, admits a complete (ultra)metric structure on the set <nobr><i>pro</i>-<font face="Brush Script MT, Script, Times New Roman">A</font>(<b>X</b>, <b>Y</b>).</nobr> The corresponding hom-bifunctor is not, generally, an internal <i>Hom</i>. However, there exists a subcategory of <nobr><i>pro</i>-<font face="Brush Script MT, Script, Times New Roman">A</font>, </nobr> containing <nobr><i>tow</i>-<font face="Brush Script MT, Script, Times New Roman">A</font>, </nobr> for which the hom-bifunctor is an invariant <i>Hom</i> into the category of complete metric spaces. Application to the sets <nobr><i>tow</i>-HcANR(<b>X</b>, <b>Y</b>)</nobr> yields several new interesting results concerning Borsuk's quasi-equivalence.

Pro-category; shape; quasi-equivalence; semi-stability; complete metric; compactum; FANR; ANR.

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