Property C, refinable maps and dimension raising maps

Topology Proceedings 10 (1985) pp. 293-303: REFINABLE MAPS AND THE PROXIMATE FIXED POINT PROPERTY

David Maps and Hausdorff Dimension

David maps are generalizations of classical planar quasiconformal maps for which the dilatation is allowed to tend to infinity in a controlled fashion. In this note we examine how these maps distort Hausdorff dimension. We show: – Given α and β in [0, 2] , there exists a David map φ: C → C and a compact set Λ such that dimH Λ = α and dimH φ(Λ) = β . – There exists a David map φ: C → C such that...

C*-Extreme Points and C*-Faces oF the Epigraph iF C*-Affine Maps in *-Rings

Abstract. In this paper, we define the notion of C*-affine maps in the unital *-rings and we investigate the C*-extreme points of the graph and epigraph of such maps. We show that for a C*-convex map f on a unital *-ring R satisfying the positive square root axiom with an additional condition, the graph of f is a C*-face of the epigraph of f. Moreover, we prove som...

Dimension groups for interval maps

With each piecewise monotonic map τ of the unit interval, a dimension triple is associated. The dimension triple, viewed as a Z[t, t−1] module, is finitely generated, and generators are identified. Dimension groups are computed for Markov maps, unimodal maps, multimodal maps, and interval exchange maps. It is shown that the dimension group defined here is isomorphic to K0(A), where A is a C*-al...

Maps Having the Bula Property

Every open continuous map f from a space X onto a paracompact C-space Y admits two disjoint closed sets F0, F1 ⊂ X , with f(F0) = Y = f(F1), provided all fibers of f are infinite and C∗-embedded in X . Applications are demonstrated for the existence of “disjoint” usco multiselections of set-valued l.s.c. mappings defined on paracompact C-spaces, and for special type of factorizations of open co...