کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4661516 | 1344433 | 2007 | 6 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Lower and upper topologies in the Hausdorff partial order on a fixed set
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
هندسه و توپولوژی
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چکیده انگلیسی
In the partial order of Hausdorff topologies on a fixed infinite set there may exist topologies τ⊊σ in which there is no Hausdorff topology μ satisfying σ⊊μ⊊τ. τ and σ are lower and upper topologies in this partial order, respectively. Alas and Wilson showed that a compact Hausdorff space cannot contain a maximal point and therefore its topology is not lower. We generalize this result by showing that a maximal point in an H-closed space is not a regular point. Furthermore, we construct in ZFC an example of a countably compact, countably tight lower topology, answering a question of Alas and Wilson. Finally, we characterize topologies that are upper in this partial order as simple extension topologies.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Topology and its Applications - Volume 154, Issue 3, 1 February 2007, Pages 619-624
Journal: Topology and its Applications - Volume 154, Issue 3, 1 February 2007, Pages 619-624