Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 1 of 1
Full-Text Articles in Mathematics
The Topology Of Surface Mediatrices, James Bernhard, J. J. P. Veerman
The Topology Of Surface Mediatrices, James Bernhard, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
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 …