Homeomorphisms of R and the Davey Space


  • Sheila Carter University of Leeds
  • F.J. Craveiro de Carvalho Universidade de Coimbra




Davey space, Homeomorphism group, Cantor set


Up to homeomorphism, there are 9 topologies on a three point set {a, b, c}. Among the resulting topological spaces we have the so called Davey space, where the only non-trivial open set is, let us say, {a}. This is an interesting topological space to the extent that every topological space can be embedded in a product of Davey spaces. In this note we will consider the problem of obtaining the Davey space as a quotient R/G, where G is a suitable homeomorphism group. The present work can be regarded as a follow-up to some previous work done by one of the authors and Bernd Wegner.


Download data is not yet available.

Author Biographies

Sheila Carter, University of Leeds

School of Mathematics

F.J. Craveiro de Carvalho, Universidade de Coimbra

Departamento de Matemática


F. J. Craveiro de Carvalho and BerndWegner, Locally Sierpinski spaces as interval quotients, Kyungpook Math. J. 42 (2002), 165-169.

Ryszard Engelking, General Topology, Heldermann Verlag, 1989.

Sidney A. Morris, Are finite topological spaces worthy of study?, Austral. Math. Soc. Gazette 11 (1984), 563-564.

James R. Munkres, Topology, a first course, Prentice-Hall, Inc., 1975.

Stephen Willard, General Topology, Addison-Wesley, Inc., 1970


How to Cite

S. Carter and F. Craveiro de Carvalho, “Homeomorphisms of R and the Davey Space”, Appl. Gen. Topol., vol. 5, no. 1, pp. 91–96, Apr. 2004.



Regular Articles