Compactness of Complete Mappings and Its Connections with Various Kinds of Nonconnectednesses of Continuous Mappings

D. K. Musaev

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: We give some necessary and sufficient conditions for compactness of tubularly (weakly) $\Pi$-complete and (weakly) $\Pi$-complete mappings that generalize compact mappings in the class of Tychonoff mappings and still have many important properties of compact mappings. We study the relationship between complete mappings and various types of nonconnectednesses of continuous mappings.

Key words: tubularly (weakly) $\Pi$-complete mapping, tubularly ($O$-$C$)-finite mapping, tubularly ($O$-$C$)-compact mapping, (weakly) $\Pi$-complete mapping.

UDC: 515.12

Received: 30.12.2004

 English version: Siberian Advances in Mathematics, 2006, 16:2, 108–120

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