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generalized Hurewicz fundamental theorem (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.



"generalized Hurewicz fundamental theorem" is owned by bci1.

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Other names:  extended Hurewicz fundamental theorem
Also defines:  connected CW-complex, homotopy groups, homology groups, Hurewicz fundamental theorem
Keywords:  generalized Hurewicz fundamental theorem

Cross-references: isomorphism, topological, Hurewicz theorem
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This is version 3 of generalized Hurewicz fundamental theorem, born on 2009-05-01, modified 2009-05-01.
Object id is 704, canonical name is GeneralizedHurewiczFundamentalTheorem.
Accessed 1370 times total.

Classification:
Physics Classification: 00. (GENERAL)
 02. (Mathematical methods in physics)
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