This article is cited in 12 papers

Characterization of Complete Mappings by Means of Morphisms into Zero-Dimensional Mappings

D. K. Musaev

Romanovskii Mathematical Institute of the National Academy of Sciences of Uzbekistan

Abstract: In this article, as in the case of $\Pi$-complete spaces, in particular, superparacompact and bicompact spaces, we prove that all components of tubularly (weakly) $\Pi$-complete mappings (in particular, of (weakly) $\Pi$-complete and superparacompact mappings) coincide with their quasicomponents, are compact, and each of their neighborhoods includes a clopen neighborhood. We also give characterizations of tubularly (weakly) $\Pi$-complete mappings by using morphisms and embeddings.
Furthermore, we generalize the Shura-Bura lemma on the components of bicompacta to bicompact mappings.

Key words: tubularly $\Pi$-complete mapping, $\Pi$-complete mapping, morphism, embedding, quasicomponent, component.

UDC: 515.12

Received: 03.07.2003

 English version: Siberian Advances in Mathematics, 2005, 15:2, 44–67

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