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

Abstract

Let $ℝ$ be the field of real numbers and ${ℝ}^n$ be the $n$-dimensional vector space over $ℝ$, where . Let $X$ be a Tyhonoff topological space and assume that it has at least two elements. For natural actions on ${ℝ}^n$ 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 ${ℝ}^n$ are investigated. Complete systems of global invariants of a topological immersion of $X$ in the space ${ℝ}^n$ are obtained for these groups. Complete systems of relations between elements of the complete systems of invariants are investigated.