A note on singular homology groups of infinite products of compacta

Volume 175 / 2002

Kazuhiro Kawamura Fundamenta Mathematicae 175 (2002), 285-289 MSC: Primary 55N10; Secondary 55Q15. DOI: 10.4064/fm175-3-5


Let $n$ be an integer with $n \geq 2$ and $\{X_{i}\}$ be an infinite collection of $(n-1)$-connected continua. We compare the homotopy groups of ${\mit\Sigma} (\prod _{i}X_{i})$ with those of $\prod _{i}{\mit\Sigma} X_{i}$ (${\mit\Sigma}$ denotes the unreduced suspension) via the Freudenthal Suspension Theorem. An application to homology groups of the countable product of the $n( \geq 2)$-sphere is given.


  • Kazuhiro KawamuraInstitute of Mathematics
    University of Tsukuba
    Tsukuba, Ibaraki 305-8071, Japan

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