Using the generalized dimension theory of topological spaces for locally compact Abelian topological groups, the conditions were investigated so that the dimension of an arbitrary locally compact abelian group may equal the dimension of its dual locally compact Abelian group. While these dimension functions show all kinds of topological behavior in arbitrary topological spaces, they behave well for separable metric spaces and for locally compact topological groups where these dimension functions coincide and can be used interchangeably.

Key words: Abelian group, Equidimensional, Locally compact.