On pseudocompact, countably compact, locally bicompact mappings, and $k$-mappings

Yu. N. Mironova

Moscow State Financial Academy

Abstract: 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.

Keywords: pseudocompactness, countable compactness, local bicompactness, $k$-mapping.

UDC: 515.1

Received: 16.10.2001

 English version: Siberian Mathematical Journal, 2002, 43:5, 899–909

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