Separation properties of continuous maps in codimension 1 and geometrical applications

Abstract Nuno Ballesteros, J.J. and M.C. Romero Fuster, Separation properties of continuous maps in codimension 1 and geometrical applications, Topology and its Applications 46 (1992) 107-111. We show that the image of a proper closed continuous map, f , from an n -manifold X to an ( n + 1)-manifold Y , such that H 1 (Y; Z 2 ) =0 , separates Y into at least two connected components provided the self-intersections set of f is not dense in any connected component of Y . We also obtain some geometrical applications.