On the dimension of certain totally disconnected spaces

Academic Article

Abstract

  • It is well known that there exist separable, metrizable, totally disconnected spaces of all dimensions. In this note we introduce the notion of an almost O-dimensional space and prove that every such space is a totally disconnected subspace of an R-tree and, hence, at most 1-dimensional. As applications we prove that the spaces of homeomorphisms of the universal Menger continua are 1-dimensional and that hereditarily locally connected spaces have dimension at most two. © 1994 American Mathematical Society.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Oversteegen LG; Tymchatyn ED
  • Start Page

  • 885
  • End Page

  • 891
  • Volume

  • 122
  • Issue

  • 3