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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)

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