Homeomorphisms of R and the Davey Space

Sheila Carter, F.J. Craveiro de Carvalho


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.


Davey space; Homeomorphism group; Cantor set

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Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt