Geodesic
Characterization of Complete Mappings by Means of Morphisms into Zero-Dimensional Mappings
Matematičeskie trudy, Tome 7 (2004) no. 2, pp. 72-97.

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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. 
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D. K. Musaev. Characterization of Complete Mappings by Means of Morphisms into Zero-Dimensional Mappings. Matematičeskie trudy, Tome 7 (2004) no. 2, pp. 72-97. http://geodesic.mathdoc.fr/item/MT_2004_7_2_a2/

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