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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Katsuya Eda and Kazuhiro Kawamura
Journal: Proc. Amer. Math. Soc. 128 (2000), 1487-1495
MSC (1991): Primary 55N10, 55N05
Published electronically: December 8, 1999
MathSciNet review: 1712917
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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: http://dx.doi.org/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
Published electronically: December 8, 1999
Communicated by: Ralph Cohen
Article copyright: © Copyright 2000 American Mathematical Society