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Physical Sciences and Mathematics Commons

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Applied Mathematics

University of Dayton

Baire

Publication Year

Articles 1 - 2 of 2

Full-Text Articles in Physical Sciences and Mathematics

Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn Jan 2010

Linearly Ordered Topological Spaces And Weak Domain Representability, Joe Mashburn

Mathematics Faculty Publications

It is well known that domain representable spaces, that is topological spaces that are homeomorphic to the space of maximal elements of some domain, must be Baire. In this paper it is shown that every linearly ordered topological space (LOTS) is homeomorphic to an open dense subset of a weak domain representable space. This means that weak domain representable spaces need not be Baire.


A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn Jan 2007

A Comparison Of Three Topologies On Ordered Sets, Joe Mashburn

Mathematics Faculty Publications

We introduce two new topologies on ordered sets: the way below topology and weakly way below topology. These are similar in definition to the Scott topology, but are very different if the set is not continuous. The basic properties of these three topologies are compared. We will show that while domain representable spaces must be Baire, this is not the case with the new topologies.