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Hereditary topological categories and topological universes. (English) Zbl 0621.54007
Topological constructs are hereditary (i.e. have hereditary quotients and coproducts) if and only if partial morphisms are representable (by suitable one-point extensions). The author thoroughly investigates one- point extensions to provide useful criteria which help to decide whether a given topological construct is hereditary or not. He then applies his results to the investigation of bi(co)reflective subcategories of hereditary topological constructs. He supplies necessary and sufficient conditions for bi(co)reflective full subconstructs of hereditary topological constructs to be hereditary. In the reflective case, preservation of certain subobjects by the reflector is a sufficient and - in case the subcategory is finally dense - also a necessary condition.
Reviewer: H.Herrlich

MSC:
54B30 Categorical methods in general topology
18B25 Topoi
18A22 Special properties of functors (faithful, full, etc.)
54B10 Product spaces in general topology
18D99 Categorical structures
54A05 Topological spaces and generalizations (closure spaces, etc.)
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