Decompositions of {mathbb {R}^n, n ge 4} , into Convex Sets Generate Codimension 1 Manifold Factors |
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| Authors: | Denise M. Halverson Dušan Repovš |
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| Affiliation: | 1. Department of Mathematics, Brigham Young University, Provo, UT, 84602, U.S.A.
2. Faculty of Education and Faculty of Mathematics and Physics, University of Ljubljana, P.O. Box 2964, Ljubljana, 1001, Slovenia
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| Abstract: | We show that if G is an upper semicontinuous decomposition ${mathbb {R}^n, n ge 4}$ , into convex sets, then the quotient space ${mathbb {R}^n/G}$ is a codimension 1 manifold factor. In particular, we show that ${mathbb {R}^n/G}$ has the disjoint arc-disk property. |
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