Eine charakterisierung epireflektiver unterkategorien einer kategorie mit inversionseigenschaft

Abstract

A compact topological space is well known to be zero-dimensional if and only if each of its quasi-components consists only of a single point. This fact will be generalized by means of category theory. It results that this theorem is valid, because the categoryK of compact spaces (and continuous maps) has the inversion property (i. e. everyK-bimorphism is aK-isomorphism). This result is obtained by a new characterization of the epireflective hull of a (full) subcategory of a complete, locally and colocally small category with inversion property.