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On extension of functors. (English) Zbl 1265.18010
This paper is about Chigogidze like extensions of functors in the category \(\text{Comp}\) of compact Hausdorff spaces on the category \(\text{Tych}\) of Tychonoff spaces and continuous maps. Let \(F\:\text{Comp}\to \text{Comp}\) be any functor in Comp: a new functor \(F_{\beta }\:\text{Tych} \to \text{Tych}\) is defined. First, the preservation of embeddings via \(F_{\beta }\) is discussed by means of the so-called 1-preimages preservation property. This property is further investigated in Section 3. Second, assuming that \(F\) is a strongly convex functor, the complete topological classification of the pair \((FX, F_{\beta }Y)\) where \(X\) is a metrizable compactum and \(Y\) is its proper dense \(G_{\delta }\)-subset is obtained.
Reviewer: Jan Paseka (Brno)

18B30 Categories of topological spaces and continuous mappings (MSC2010)
54B30 Categorical methods in general topology
57N20 Topology of infinite-dimensional manifolds