Strongly locally homogeneous generalized continua of finite cohomological dimension.

The notion of a V n -continuum was introduced by Alexandroff [1] as a generalization of the concept of n -manifold. In this note we consider the cohomological analogue of V n -continuum and prove that any strongly locally homogeneous generalized continuum X with cohomological dimension dim G ⁡ X = n is a generalized V n -space with respect to the cohomological dimension dim G. In particular, every strongly locally homogeneous continuum of covering dimension n is a V n -continuum in the sense of Alexandroff. This provides a partial answer to a question raised in [12]. An analog of the Mazurkiewicz theorem that no subset of covering dimension ≤ n − 2 cuts any region of the Euclidean n -space is also obtained for strongly locally homogeneous generalized continua X of cohomological dimension dim G ⁡ X = n. [ABSTRACT FROM AUTHOR]