Abstract
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.
Citation
Taras Banakh. Dušan Repovš. "Universal nowhere dense subsets of locally compact manifolds." Algebr. Geom. Topol. 13 (6) 3687 - 3731, 2013. https://doi.org/10.2140/agt.2013.13.3687
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