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Dimensional Properties of Generalized Manifolds and Some Properties of Weakly Net-Like Spaces

Abstract We consider dimensional type functions defined on the class of π-bicompact spaces. Using these functions, the dimensional properties of generalized manifolds are studied. The class of weakly net-like spaces is introduced, which is a natural generalization of net-like spaces in the sense of V. V. Proizvolov and the behavior of this class is studied in the case of (monotone, open) mappings of special type. Generalizations of V. V. Proizvolov's theorems are obtained for weakly net-like spaces.