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On a theorem of Fleischer

Part of: Special properties

Published online by Cambridge University Press:  09 April 2009

G. Mehta
G. Mehta
Affiliation:
Departments of Economics and of Mathematics, University of Queensland, St. Lucia, Queensland, 4067, Australia
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Abstract

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Fleischer proved that a linearly ordered set that is separable in its order topology and has countably many jumps is order-isomorphic to a subset of the real numbers. The object of this paper is to extend Fleischer's result and to prove it in a different way. The proof of the theorem is based on Nachbin's extension to ordered topological spaces of Urysohn's separation theorem in normal topological spaces.

MSC classification

Secondary: 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 2 , April 1986 , pp. 261 - 266
Copyright
Copyright Australian Mathematical Society 1986

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