Revista Colombiana de Matemáticas
Print version ISSN 0034-7426
This paper we provides an alternative proof of Hurewicz theorem when the topological space X is a CW-complex. Indeed, we show that if X0 C X1 C ... Xn-1 C Xn = X is the CW decomposition of X, then the Hurewicz homomorphism ∏n+1 (Xn+1,Xn) → Hn+1 (Xn+1,Xn) is an isomorphism, and together with a result from Homological Algebra we prove that if X is (n-1)-connected, the Hurewicz homomorphism ∏n (X) → Hn (X) is an isomorphism.
Keywords : Hurewicz homomorphism; CW-complexes; exact sequence; homotopic groups; homology groups.