Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 6 (2013), 3687-3731.
Universal nowhere dense subsets of locally compact manifolds
In each manifold modeled on a finite- or infinite-dimensional cube , , we construct a closed nowhere dense subset (called a spongy set) which is a universal nowhere dense set in in the sense that for each nowhere dense subset there is a homeomorphism such that . The key tool in the construction of spongy sets is a theorem on the topological equivalence of certain decompositions of manifolds. A special case of this theorem says that two vanishing cellular strongly shrinkable decompositions of a Hilbert cube manifold are topologically equivalent if any two nonsingleton elements and of these decompositions are ambiently homeomorphic.
Algebr. Geom. Topol., Volume 13, Number 6 (2013), 3687-3731.
Received: 8 February 2012
Accepted: 21 May 2013
First available in Project Euclid: 19 December 2017
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Banakh, Taras; Repovš, Dušan. Universal nowhere dense subsets of locally compact manifolds. Algebr. Geom. Topol. 13 (2013), no. 6, 3687--3731. doi:10.2140/agt.2013.13.3687. https://projecteuclid.org/euclid.agt/1513715745