Published online by Cambridge University Press: 24 October 2008
In this paper we study the group of pointed proper homotopy classes of proper pointed maps from (ℝn+1, 0) to a pointed σ-compact space (X, x) and prove the existence of a diagram of exact sequences linking the groups with the Brown—Grossman groups , the Steenrod groups πn(X) and the classical Hurewicz homotopy groups πn(X).