Infima of quasi-uniform anti-atoms |
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Authors: | Eliza P de Jager Hans-Peter A Künzi |
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Institution: | Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch 7701, South Africa |
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Abstract: | Let (q(X),⊆) denote the lattice consisting of the set q(X) of all quasi-uniformities on a set X, ordered by set-theoretic inclusion ⊆. We observe that a quasi-uniformity on X is the supremum of atoms of (q(X),⊆) if and only if it is totally bounded and transitive. Each quasi-uniformity on X that is totally bounded or has a linearly ordered base is shown to be the infimum of anti-atoms of (q(X),⊆). Furthermore, each quasi-uniformity U on X such that the topology of the associated supremum uniformity Us is resolvable has the latter property. |
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Keywords: | 54E15 54E05 06B05 |
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