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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, 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: theorem
There are 9 references to this object.

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 451 times total.

Classification:

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

Pending Errata and Addenda

None.

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