Affine invariants of an immersion of a topological space in the n-dimensional real vector space

Let R be the field of real numbers and Rn be the n-dimensional vector space over R, where n > 1. Let X be a Tyhonoff topological space and assume that it has at least two elements. For natural actions on Rn of the group of all non-degenerate linear transformations, the group of all affine transformations and their some subgroups, problems of equivalence of topological immersions of X in Rn are investigated. Complete systems of global invariants of a topological immersion of X in the space Rn are obtained for these groups. Complete systems of relations between elements of the complete systems of invariants are investigated.