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Universal nowhere dense
subsets of locally compact manifolds
Taras Banakh and Dušan Repovš |
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Algebraic & Geometric Topology 13 (2013) 3687–3731
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Abstract |
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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. |
Keywords
Universal nowhere dense subset, Sierpiński carpet, Menger
cube, Hilbert cube manifold, $n$–manifold, tame ball, tame
decomposition
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Mathematical Subject Classification 2010
Primary: 57N20, 57N40
Secondary: 57N45, 57N60
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References |
Publication
Received: 8 February 2012
Accepted: 21 May 2013
Published: 16 October 2013
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Authors |
| Taras Banakh | |
| Department of Geometry and
Topology Ivan Franko National University of Lviv 1 Universytetska str Lviv, 79000 Ukraine and Instytut Matematyki Jan Kochanowski University in Kielce 15 Swietokrzyska str 25-406 Kielce Poland |
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| http://www.franko.lviv.ua/faculty/mechmat/Departments/Topology/bancv.html | |
| Dušan Repovš | |
| Faculty of Education and Faculty of
Mathematics and Physics University of Ljubljana Kardeljeva ploscad 16 1000 Ljubljana Slovenia |
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| http://www.fmf.uni-lj.si/~repovs/ | |
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