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Title of article :
Lower and upper topologies in the Hausdorff partial order on a fixed set
Author/Authors :
Carlson، نويسنده , , Nathan، نويسنده ,
Issue Information :
دوماهنامه با شماره پیاپی سال 2007
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Abstract :
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.
Keywords :
Upper topology , H-closed , Countably compact , Lower topology , Countably tight
Journal title :
Topology and its Applications
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Link To Document :