کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4661458 | 1344429 | 2007 | 15 صفحه PDF | دانلود رایگان |
Given a pair of distinct points p and q in a metric space with distance d, the mediatrix is the set of points x such that d(x,p)=d(x,q). In this paper, we examine the topological structure of mediatrices in connected, compact, closed 2-manifolds whose distance function is inherited from a Riemannian metric. We determine that such mediatrices are, up to homeomorphism, finite, closed simplicial 1-complexes with an even number of incipient edges emanating from each vertex. Using this and results from [J.J.P. Veerman, J. Bernhard, Minimally separating sets, mediatrices and Brillouin spaces, Topology Appl., in press], we give the classification up to homeomorphism of mediatrices on genus 1 tori (and on projective planes) and outline a method which may possibly be used to classify mediatrices on higher-genus surfaces.
Journal: Topology and its Applications - Volume 154, Issue 1, 1 January 2007, Pages 54-68