Cohomologia de Alexander-Spanier e o teorema de Ballesteros

Abstract

In the present work, we prove a more general version of Jordan’s Curve Theorem. Supposing that f : X ---> Y is a proper map, where X and Y are topological manifolds of dimensions n and n + 1 , respectively, and more hypotheses about the set of f ’s self intersections, we get a formula for the number of connected components of the complement of f(X) in Y . For this, we will present an alternative cohomology theory and prove its main properties.