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On pseudocompact, countably compact, locally bicompact mappings, and \(k\)-mappings. (Russian, English) Zbl 1018.54010

Sib. Mat. Zh. 43, No. 5, 1115-1129 (2002); translation in Sib. Math. J. 43, No. 5, 899-909 (2002).
Summary: We consider various definitions of a pseudocompact mapping and the basic properties of pseudocompact mappings. Moreover, we consider the definition of countable compactness of a continuous mapping and study the properties of a countably compact mapping similar to the corresponding properties for countably compact spaces and also the interrelation between countable compactness and pseudocompactness of mappings. We also extend the notions of local bicompactness and \(k\)-space to continuous mappings.

MSC:

54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54D30 Compactness
54C05 Continuous maps
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