# Representing Quasi-Orders by Embeddability Ordering of Families of Topological Spaces

## Proceedings of the American Mathematical Society / v.127 no.5. 1999, pp.1275-1279 window.___gcfg = {lang: 'ko'}; (function() { var po = document.createElement('script'); po.type = 'text/javascript'; po.async = true; po.src = 'https://apis.google.com/js/platform.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(po, s); })();

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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.

Keyword : Primary 06A06, 54H10 . Partial order . Quasi-order . Ordering by embeddability

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