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The surjectivity of the canonical homomorphism from singular homology to Cech homology

Author(s): Katsuya Eda; Kazuhiro Kawamura
Journal: Proc. Amer. Math. Soc. 128 (2000), 1487-1495.
MSC (1991): Primary 55N10, 55N05
Posted: December 8, 1999
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Abstract: Let $X$ be a locally $n$-connected compact metric space. Then, the canonical homomorphism from the singular homology group $H_{n+1}(X)$ to the Cech homology group $\check{H}_{n+1}(X)$ is surjective. Consequently, if a compact metric space $X$ is locally connected, then the canonical homomorphism from $H_1(X)$ to ${\check H}_1(X)$ is surjective.

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Additional Information:

Katsuya Eda
Affiliation: School of Science and Engineering, Waseda University, Tokyo 169-0072, Japan
Email: eda@logic.info.waseda.ac.jp

Kazuhiro Kawamura
Affiliation: Institute of Mathematics, University of Tsukuba, Tsukuba 305, Japan
Email: kawamura@math.tsukuba.ac.jp

DOI: 10.1090/S0002-9939-99-05670-1
PII: S 0002-9939(99)05670-1
Keywords: Singular homology, \v Cech homology, canonical homomorphism, surjective
Received by editor(s): July 29, 1997
Posted: December 8, 1999
Communicated by: Ralph Cohen
Copyright of article: Copyright 2000, American Mathematical Society

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