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Vietoris-Begle Theorem and Spectra

Jerzy Dydak and George Kozlowski
Proceedings of the American Mathematical Society
Vol. 113, No. 2 (Oct., 1991), pp. 587-592
DOI: 10.2307/2048547
Stable URL: http://www.jstor.org/stable/2048547
Page Count: 6
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Abstract

The following generalization of the Vietoris-Begle Theorem is proved: Suppose $\{E_k \}_{k \geq 1}$ is a CW spectrum and f: X' → X is a closed surjective map of paracompact Hausdorff spaces such that $\operatorname{Ind} X = m < \infty$. If f*: Ek(x) → Ek(f-1(x)) is an isomorphism for all x ∈ X and k = m0, m0 + 1,..., m0 + m, then f*: En(X) → En(X') is an isomorphism and f*: En + 1(X) → En + 1(X') is a monomorphism for n = m0 + m.

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