Homeomorphisms of R and the Davey Space

Sheila Carter, F.J. Craveiro de Carvalho

Abstract

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.


Keywords

Davey space; Homeomorphism group; Cantor set

Full Text:

PDF

References

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

Abstract Views

930
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

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