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- W1508094908 abstract "AbstractA.Chigogidze defined for each normal functor on the category Comp an extensionwhich is a normal functor on the category Tych. We consider this extension for anyfunctor on the category Comp and investigate which properties it preserves from thedefinition it preserves from the definition of normal functor. We investigate as well sometopological properties of such extension. Introduction. The general theory of functors acting in the category Compof compactHausdorff spaces (compacta) and continuous mappings was founded by E.V. Shchepin [15]. Hedistinguished some elementary properties of such functors and defined the notion of normalfunctor that has become very fruitful. The class of normal functors includes many classicalconstructions: the hyperspace exp, the functor of probability measures P, the power functorand many other functors (see [13],[9] for more details). But some important functors do notsatisfy some of the properties from the Shchepin list. Omitting some properties we obtain widerclasses of functors such as weakly normal functors and almost normal functors.The properties from the definition of normal functor could be easily generalized for the func-tors on the category Tychof Tychonov spaces and continuous maps. Let us remark that Tychcontains Compas a subcategory. A.Chigogidze defined for each normal functor on the categoryCompan extension which is a normal functor on the category Tych[6]. This extension couldbe considered for any functor on the category Comp. But the situation is more complicated forwider classes of functors. For example, the extension of the projective power functor (whichis weakly normal) does not preserve embeddings, which makes such extension useless (see for1" @default.
- W1508094908 created "2016-06-24" @default.
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- W1508094908 date "2011-06-02" @default.
- W1508094908 modified "2023-09-27" @default.
- W1508094908 title "On Extension of Functors" @default.
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