A Riemann-Roch Theorem for Compact Spaces

Following the work of Grothendieck which shows that we have a Riemann-Roch theorem for certain morphisms of algebraic varieties and of Hirzebruch and Atiyah for certain morphisms of differentiable varieties we will show that we have a Riemann-Roch theorem for continuous applications between compact spaces satisfying certain conditions within the framework of the topological K-theory of compact spaces.