The homology of spaces of simple topological measures

Abstract

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 qspace 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.

The median in multidimensional spaces

“…All monotone continuous maps are solid variables. In [12] it is shown that the solid variables in median-spaces are necessarily monotone. Hence for median-spaces the two concepts coincide.…”

Simple topological measures and a lifting problem

“…According to Ørjan Johansen and Alf Birger Rustad the map λ : X * → X * int is a deformation retraction so the inclusion X * int ⊆ X * of the intrinsic simple topological measures into all the simple topological measures induces isomorphisms on theČech cohomology groups (see [8]). It follows that X * is connected if and only if X * int is connected.…”