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Joins of topologies homeomorphic to the rationals

Part of: Spaces with richer structures

Published online by Cambridge University Press:  09 April 2009

A. J. Jayanthan  and
V. Kannan
A. J. Jayanthan
Affiliation:
School of Mathematics & Computer/Information SciencesUniversity of HyderabadHyderabad-500 134, India
V. Kannan
Affiliation:
School of Mathematics & Computer/Information SciencesUniversity of HyderabadHyderabad-500 134, India
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Abstract

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Let Q be the space of all rational numbers and (X, τ) be a topological space where X is countably infinite. Here we prove that (1) τ is the join of two topologies on X both homeomorphic to Q if and only if τ is non-compact and metrizable, and (2) τ is the join of topologies on X each homeomorphic to Q if and only if τ is Tychonoff and noncompact.

Keywords

metric spacesjoins of topologiescountable spaces.

MSC classification

Secondary: 54E35: Metric spaces, metrizability
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 2 , October 1989 , pp. 256 - 262
Copyright
Copyright © Australian Mathematical Society 1989

References

[1]Sierpiński, W., ‘Sur une propriété topologique des ensembles denombrables dense en soi’, Fund. Math. 1 (1920), 11–16.CrossRefGoogle Scholar
[2]Willard, S., General topology, (Addison-Wesley, 1970).Google Scholar