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Skeletons and Central Sets 总被引:1,自引:0,他引:1
Let be an open proper subset of Rn. Its skeleton is the setof points with more than one nearest neighbour in the complementof its central set is the set of centres in maximal open ballsincluded in . Intuitively, if we think of as a land mass inwhich height is proportional to distance from the sea, its skeletonand central set can be thought of as corresponding to ridgesin the mountains of . In this note I discuss the metric andtopological properties of such sets. I show that any skeletonin Rn is F, and has dimension at most n 1, by any ofthe usual measures of dimension; that if is bounded and connected,its skeleton and central set are connected; and that separatesRn iff its skeleton does iff its central set does. Any centralset in Rn is a G set of topological dimension at most n 1. In the plane, I show that both skeletons and central setsare locally path-connected, and indeed include many paths offinite length. For any , its central set includes its skeleton;I give examples to show that the central set can be significantlylarger than the skeleton. 1991 Mathematics Subject Classification:54F99. 相似文献
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Mertz C Vellidis CE Alarcon R Barkhuff DH Bernstein AM Bertozzi W Burkert V Chen J Comfort JR Dodson G Dolfini S Dow K Farkhondeh M Finn JM Gilad S Gothe RW Jiang X Joo K Kaloskamis NI Karabarbounis A Kelly JJ Kowalski S Kunz C Lourie RW McIntyre JI Milbrath BD Miskimen R Mitchell JH Papanicolas CN Perdrisat CF Sarty AJ Shaw J Soong SB Tieger D Tschalaer C Turchinetz W Ulmer PE Van Verst S Warren GA Weinstein LB Williamson S Woo RJ Young A 《Physical review letters》2001,86(14):2963-2966
High-precision 1H(e,e'p)pi(0) measurements at Q2 = 0.126 (GeV/c)2 are reported, which allow the determination of quadrupole amplitudes in the gamma*N-->Delta transition; they simultaneously test the reliability of electroproduction models. The derived quadrupole-to-dipole ( I = 3/2) amplitude ratios, R(SM) = (-6.5+/-0.2(stat+sys)+/-2.5(mod))% and R(EM) = (-2.1+/-0.2(stat+sys)+/-2.0(mod))%, are dominated by model error. Previous R(SM) and R(EM) results should be reconsidered after the model uncertainties associated with the method of their extraction are taken into account. 相似文献