The simple topological measures X* 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* are calculated. For a q-space X, X* is shown to be a q-space. The homology of X* when X is the annulus is calculated. The homology of X* when X is a more general genus one space is investigated. In particular, X* for the torus is shown to have a retract homeomorphic to an infinite product of circles.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-1-2,
author = {\O . Johansen and A. B. Rustad},
title = {The homology of spaces of simple topological measures},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {19-43},
zbl = {1077.28013},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-1-2}
}
Ø. Johansen; A. B. Rustad. The homology of spaces of simple topological measures. Fundamenta Mathematicae, Tome 177 (2003) pp. 19-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm177-1-2/