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Extensions of mappings. II. (English) Zbl 0719.54014
Topics in general topology, North-Holland Math. Libr. 41, 41-80 (1989).
[For the entire collection see Zbl 0684.00017.]
In this expository paper the author discusses C-, \(C^*\)-, and \(P^ m\)- embedding of subspaces of topological spaces. These concepts, which relate to the extension to X of certain continuous functions defined on a subspace A of X, are related to extensions to X of certain “normal covers” of A. To this end normal covers are discussed in detail. The \(C^*\)-embedding of unions of \(C^*\)-embedded subspaces of a space, and \(C^*\)-embedding in product spaces, are also discussed in detail. The paper ends with a discussion of the homotopy extension property.

54C20 Extension of maps
54C45 \(C\)- and \(C^*\)-embedding
54-02 Research exposition (monographs, survey articles) pertaining to general topology
55P05 Homotopy extension properties, cofibrations in algebraic topology
54B10 Product spaces in general topology
54D20 Noncompact covering properties (paracompact, Lindelöf, etc.)