Theorem Suppose X is a connected space and x is a point in X. If X{x} is a disconnected set in X, then x is a cut-point of X [1, 2].

0.0.1 Examples

  1. 1.

    Any point of with the usual topology is a cut-point.

  2. 2.

    If X is a normed vector spacePlanetmathPlanetmath with dimX>1, then X has no cut-points [1].


  • 1 G.J. Jameson, TopologyMathworldPlanetmath and Normed Spaces, Chapman and Hall, 1974.
  • 2 L.E. Ward, Topology, An Outline for a First Course, Marcel Dekker, Inc., 1972.
Title cut-point
Canonical name Cutpoint
Date of creation 2013-03-22 13:56:38
Last modified on 2013-03-22 13:56:38
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 5
Author mathcam (2727)
Entry type Definition
Classification msc 54D05
Synonym cutpoint