12 citations · 30 across the 8 of their papers we have counts for
8 papers
Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties
Denise M. Halverson, Dušan Repovš
We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecew…
Decompositions of into convex sets generate codimension 1 manifold factors
Denise M. Halverson, Dušan Repovš
We show that if is an upper semicontinuous decomposition of , , into convex sets, then the quotient space is a codimension one manifold…
The Homogeneous Property of the Hilbert Cube
Denise M. Halverson, David G. Wright
We demonstrate the homogeneity of the Hilbert Cube. In particular, we construct explicit self-homeomorphisms of the Hilbert cube so that given any two points, a homeomorphism movin…
Survey on the Generalized R. L. Moore Problem
Denise M. Halverson, Dušan Repovš
We give an updated extended survey of results related to the celebrated unsolved generalized R. L. Moore problem. In particular, we address the problem of characterizing codimensio…
Locally -homogeneous Busemann -spaces
V. N. Berestovskiĭ, D. M. Halverson, D. Repovš
We present short proofs of all known topological properties of general Busemann -spaces (at present no other property is known for dimensions more than four). We prove that all…
Detecting codimension one manifold factors with topographical techniques
Denise M. Halverson, Dušan Repovš
We prove recognition theorems for codimension one manifold factors of dimension . In particular, we formalize topographical methods and introduce three ribbons properties…