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Representing quasi-orders by embeddability ordering of families of topological spaces


Authors: A. E. McCluskey and T. B. M. McMaster
Journal: Proc. Amer. Math. Soc. 127 (1999), 1275-1279
MSC (1991): Primary 06A06, 54H10
DOI: https://doi.org/10.1090/S0002-9939-99-04848-0
Published electronically: January 27, 1999
MathSciNet review: 1600113
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Abstract: An elementary argument constructs, for each cardinal $\alpha$, a topological space whose subspaces, ordered by homeomorphic embeddability, can model every partial order on $\alpha$-many points. We show how to modify this procedure to deal also with quasi-orders (where the antisymmetry condition may fail), obtaining an initial estimate of the cardinality of the space then required.


References [Enhancements On Off] (What's this?)

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Additional Information

A. E. McCluskey
Affiliation: Department of Mathematics, National University of Ireland, Galway, Ireland
Email: a.mccluskey@ucg.ie

T. B. M. McMaster
Affiliation: Department of Pure Mathematics, Queen’s University of Belfast, Belfast BT7 1NN, Northern Ireland
Email: t.b.m.mcmaster@qub.ac.uk

DOI: https://doi.org/10.1090/S0002-9939-99-04848-0
Keywords: Partial order, quasi-order, ordering by embeddability
Received by editor(s): August 9, 1997
Published electronically: January 27, 1999
Communicated by: Alan Dow
Article copyright: © Copyright 1999 American Mathematical Society

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