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

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.