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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.
Ø. Johansen, and A. B. Rustad. "The homology of spaces of simple topological measures." Fundamenta Mathematicae 177.1 (2003): 19-43. <http://eudml.org/doc/282843>.
@article{Ø2003, abstract = {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.}, author = {Ø. Johansen, A. B. Rustad}, journal = {Fundamenta Mathematicae}, keywords = {topological measures; superextension; retract; q-space; compact Hausdorff space; spaces with genus zero; homology}, language = {eng}, number = {1}, pages = {19-43}, title = {The homology of spaces of simple topological measures}, url = {http://eudml.org/doc/282843}, volume = {177}, year = {2003}, }
TY - JOUR AU - Ø. Johansen AU - A. B. Rustad TI - The homology of spaces of simple topological measures JO - Fundamenta Mathematicae PY - 2003 VL - 177 IS - 1 SP - 19 EP - 43 AB - 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. LA - eng KW - topological measures; superextension; retract; q-space; compact Hausdorff space; spaces with genus zero; homology UR - http://eudml.org/doc/282843 ER -