generalized Hurewicz fundamental theorem

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 $ \pi_r (K,L) =0$ for $ 1 \leq r \leq n$ , $ (n \geq 2)$ , then $ h_\pi : \pi_n^* (K,L)\simeq H_n(K,L)$ , where $ \pi_n$ are homotopy groups, $ H_n$ are homology groups, K and L are arbitrary topological spaces, and `$ \simeq$ ' denotes an isomorphism.

Bibliography

1
Spanier, E. H.: 1966, Algebraic Topology, McGraw Hill: New York.



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