TY - JOUR
AB - Let X and Y be proper metric spaces. We show that a coarsely n-to-1 map f:X→Y induces an n-to-1 map of Higson coronas. This viewpoint turns out to be successful in showing that the classical dimension raising theorems hold in large scale; that is, if f:X→Y is a coarsely n-to-1 map between proper metric spaces X and Y then asdim(Y)≤asdim(X)+n−1. Furthermore we introduce coarsely open coarsely n-to-1 maps, which include the natural quotient maps via a finite group action, and prove that they preserve the asymptotic dimension.
AU - Austin, Kyle
AU - Virk, Ziga
ID - 521
JF - Topology and its Applications
SN - 01668641
TI - Higson compactification and dimension raising
VL - 215
ER -
TY - JOUR
AB - We generalize Brazas’ topology on the fundamental group to the whole universal path space X˜ i.e., to the set of homotopy classes of all based paths. We develop basic properties of the new notion and provide a complete comparison of the obtained topology with the established topologies, in particular with the Lasso topology and the CO topology, i.e., the topology that is induced by the compact-open topology. It turns out that the new topology is the finest topology contained in the CO topology, for which the action of the fundamental group on the universal path space is a continuous group action.
AU - Virk, Ziga
AU - Zastrow, Andreas
ID - 737
JF - Topology and its Applications
SN - 01668641
TI - A new topology on the universal path space
VL - 231
ER -