Representing quasi-orders by embeddability ordering of families of topological spaces
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- by A. E. McCluskey and T. B. M. McMaster PDF
- Proc. Amer. Math. Soc. 127 (1999), 1275-1279 Request permission
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
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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
- Received by editor(s): August 9, 1997
- Published electronically: January 27, 1999
- Communicated by: Alan Dow
- © Copyright 1999 American Mathematical Society
- 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
- MathSciNet review: 1600113