Homeomorphisms of R and the Davey Space

• Carter, Sheila ^[1] ; Craveiro de Carvalho, F.J. ^[2]
  1. [1] University of Leeds

     University of Leeds

     Reino Unido

     
  2. [2] Universidade de Coimbra

     Universidade de Coimbra

     Coimbra (Sé Nova), Portugal

     
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 5, Nº. 1, 2004, págs. 91-96
• Idioma: inglés
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• Resumen

  • 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.