Open AccessHomeomorphisms of R and the Davey Space
Author(s) -
Sheila Carter,
F. J. Craveiro de Carvalho
Publication year - 2004
Publication title -
applied general topology
Language(s) - English
Resource type - Journals
eISSN - 1989-4147
pISSN - 1576-9402
DOI - 10.4995/agt.2004.1997
Subject(s) - homeomorphism (graph theory) , mathematics , topological space , space (punctuation) , connected space , set (abstract data type) , open set , pure mathematics , group (periodic table) , quotient space (topology) , topology (electrical circuits) , product (mathematics) , quotient , discrete mathematics , combinatorics , computer science , geometry , chemistry , organic chemistry , programming language , operating system
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
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