The homology of spaces of simple topological measures

Ø. Johansen ¹   ; A. B. Rustad ¹

¹ Department of Mathematical Sciences Norwegian University of Science and Technology N-7491 Trondheim, Norway

Fundamenta Mathematicae, Tome 177 (2003) no. 1, pp. 19-43

Résumé

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.

Détail

DOI : 10.4064/fm177-1-2

Keywords: simple topological measures ast q space shown superextension properties inherited superextensions topological measures presented homology groups various subsets ast calculated q space ast shown q space homology ast annulus calculated homology ast general genus space investigated particular ast torus shown have retract homeomorphic infinite product circles