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Euclidean representations of topologically ordered spaces

Part of: Special properties

Published online by Cambridge University Press:  26 February 2010

H. B. Griffiths
H. B. Griffiths
Affiliation:
Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton, SO9 5NH
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Extract

A topological ordered space (or pospace) is a poset (X, <) with a topology on X for which the relation < is closed in the product X × X. The topology of X is then necessarily Hausdorff. The basic theory of pospaces was developed by Nachbin in his book [5]; and others have extended it, but the resulting body of knowledge is not very geometrical. There are few concrete examples, other than the unit interval I with its natural order, and Euclidean spaces (Rn, ≤), the Hilbert cube (H, ≤) (each with the vector order), and some function spaces.

MSC classification

Secondary: 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
Type
Research Article
Information
Mathematika , Volume 39 , Issue 1 , June 1992 , pp. 104 - 135
Copyright
Copyright © University College London 1992

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