A note on singular homology groups of infinite products of compacta
Volume 175 / 2002
Fundamenta Mathematicae 175 (2002), 285-289
MSC: Primary 55N10; Secondary 55Q15.
DOI: 10.4064/fm175-3-5
Abstract
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.
