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Researcher Medini, Andrea
Source CiteSeerX
Content type Text
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Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Cantor Set Topic ♦ Topology Ultrafilters Subspace ♦ Martin Axiom ♦ Countable Posets ♦ Second Part ♦ Non-principal Ultrafilter ♦ First Part ♦ Joint Work ♦ Perfect Set Property ♦ Following Topological Property ♦ Characteristic Function ♦ Countable Dense ♦ Non-principal Ultrafilters ♦ Topological Property ♦ Countable Dense Homogeneity ♦ Zamora Avil ♦ Closed Subset ♦ David Milovich
Abstract In the first part of this thesis (Chapter 1), we will identify ultrafilters on ω with subspaces of 2 ω through characteristic functions, and study their topological properties. More precisely, let P be one of the following topological properties. • P = being completely Baire. • P = countable dense homogeneity. • P = every closed subset has the perfect set property. We will show that, under Martin’s Axiom for countable posets, there exist non-principal ultrafilters U, V ⊆ 2ω such that U has property P and V does not have property P. The case ‘P = being completely Baire ’ actually follows from a result obtained independently by Marciszewski, of which we were not aware (see Theorem 1.37 and the remarks following it). Using the same methods, still under Martin’s Axiom for countable posets, we will construct a non-principal ultrafilter U ⊆ 2ω such that U ω is countable dense homogeneous. This consistently answers a question of Hruˇsák and Zamora Avilés. All of Chapter 1 is joint work with David Milovich. In the second part of the thesis (Chapter 2 and Chapter 3), we will study CLP-compactness
Educational Role Student ♦ Teacher
Age Range above 22 year
Educational Use Research
Education Level UG and PG ♦ Career/Technical Study
Learning Resource Type Thesis
Publisher Date 2013-01-01