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Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

Denise HalversonDušan Repovš — 2013

Open Mathematics

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 piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension n ≥ 4 determined by general position properties, the piecewise disjoint arc-disk...

The cell-like approximation theorem in dimension 5

Robert J. DavermanDenise M. Halverson — 2007

Fundamenta Mathematicae

The cell-like approximation theorem of R. D. Edwards characterizes the n-manifolds precisely as the resolvable ENR homology n-manifolds with the disjoint disks property for 5 ≤ n < ∞. Since no proof for the n = 5 case has ever been published, we provide the missing details about the proof of the cell-like approximation theorem in dimension 5.

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