The Stone-Cech Compactification of the Plane

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Title: The Stone-Cech Compactification of the Plane
Author: Cabbage, Brian William
Advisors: Gary Faulkner, Committee Chair
Richard Chandler, Committee Member
Jesus Rodriguez, Committee Member
Ernie Stitzinger, Committee Member
Abstract: The motivation for this dissertation came from Franco Obersnel's dissertation On Compactifications of the Set of Natural Numbers and the Half Line. In it he proves that any non-degenerate subcontinuum of the Stone Cech remainder of the half line will map onto any arbitrary continuum of weight ≤ ω₁. We are able to prove the same property for many (though not all) non-degenerate subcontinua of the Stone-Cech remainder of the plane, as well as investigating certain algebraic and topological structures on subsets of the remainder.
Date: 2006-05-04
Degree: PhD
Discipline: Mathematics
URI: http://www.lib.ncsu.edu/resolver/1840.16/5532


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