The homology of spaces of simple topological measures
Volume 177 / 2003
Fundamenta Mathematicae 177 (2003), 19-43
MSC: 28Cxx, 46M18, 54Uxx.
DOI: 10.4064/fm177-1-2
Abstract
The simple topological measures $X^{\ast }$ on a q-space $X$ are shown to be a superextension of $X$. Properties inherited from superextensions to topological measures are presented. The homology groups of various subsets of $X^{\ast }$ are calculated. For a q-space $X$, $X^{\ast }$ is shown to be a q-space. The homology of $X^{\ast }$ when $X$ is the annulus is calculated. The homology of $X^{\ast }$ when $X$ is a more general genus one space is investigated. In particular, $X^{\ast }$ for the torus is shown to have a retract homeomorphic to an infinite product of circles.
