A note on singular homology groups of infinite products of compacta

Kazuhiro Kawamura¹

¹ Institute of Mathematics University of Tsukuba Tsukuba, Ibaraki 305-8071, Japan

Fundamenta Mathematicae, Tome 175 (2002) no. 3, pp. 285-289.

Résumé

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.

Détail

DOI : 10.4064/fm175-3-5

Keywords: integer geq infinite collection n connected continua compare homotopy groups mit sigma prod those prod mit sigma mit sigma denotes unreduced suspension via freudenthal suspension theorem application homology groups countable product geq sphere given