PlanetPhysics/Generalized Hurewicz Fundamental Theorem

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Generalized Hurewicz Fundamental Theorem

The [[../ModuleAlgebraic/|Hurewicz theorem]] was generalized from connected CW-complexes to arbitrary [[../CoIntersections/|topological]] spaces and is stated as follows.

\begin{theorem} If ${\pi }_r(K,L)=0$ for $1\le r\le n$ , $(n\ge 2)$, 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 \htmladdnormallink{isomorphism {http://planetphysics.us/encyclopedia/IsomorphicObjectsUnderAnIsomorphism.html}.} \end{theorem}