Partitioning in locally connected metric spaces
by
E. D. Tymchatyn
University of Saskatchewan, Canada

A partition of a locally connected metric space is a finite collection U of closed locally connected subsets u such that the boundary of u is a Z-set for arcs in u and each two members of U meet at most in common boundary points.Moise and Bing used partitions to prove that each Peano continuum admits a compatible convex metric.i.e.a metric d such that each pair of points are joined by a subset isometric to an interval in the real line.More recently partitions have been used in the study of Menger manifolds and Nobeling manifolds.We look again at partitions with an eye towards applications in the noncompact case.

Date received: July 5, 2000