Topological aspects of poset spaces

Details Topological aspects of poset spaces Topological aspects of poset spaces

2009-12-16

arxiv.org/abs/0912.3191v1

Michigan Mathematical Journal v. 59, 2010, pp. 3-24

Mathematics

General Topology

29 pages. To be published in the Michigan Mathematical Journal

Scientific paper

10.1307/mmj/1272376025.

We study two classes of spaces whose points are filters on partially ordered sets. Points in MF spaces are maximal filters, while points in UF spaces are unbounded filters. We give a thorough account of the topological properties of these spaces. We obtain a complete characterization of the class of countably based MF spaces: they are precisely the second-countable T_1 spaces with the strong Choquet property. We apply this characterization to domain theory to characterize the class of second-countable spaces with a domain representation.

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