کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4660810 | 1344386 | 2006 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Infima of quasi-uniform anti-atoms
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
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.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 153, Issue 17, 1 November 2006, Pages 3327-3337
Journal: Topology and its Applications - Volume 153, Issue 17, 1 November 2006, Pages 3327-3337