Generalized Hurewicz Fundamental Theorem
The Hurewicz theorem was generalized from connected CW-complexes to arbitrary topological
spaces [1] and is stated as follows.
Theorem 0.1. If πr(K,L) = 0 for 1 ≤ r ≤ n , (n ≥ 2), then hπ : πn∗(K,L) ≃ H
n(K,L) ,
where πn are homotopy groups, Hn are homology groups, K and L are arbitrary topological
spaces, and ‘≃’ denotes an isomorphism.
References
[1] Spanier, E. H.: 1966, Algebraic Topology, McGraw Hill: New York.
