The Stone-Cech Compactification of the Plane

stone-cech compactification;topology;ultrafilter;hyperreals

Cabbage, Brian William ; Gary Faulkner, Committee Chair,Richard Chandler, Committee Member,Jesus Rodriguez, Committee Member,Ernie Stitzinger, Committee Member,Cabbage, Brian William ; Gary Faulkner ; Committee Chair ; Richard Chandler ; Committee Member ; Jesus Rodriguez ; Committee Member ; Ernie Stitzinger ; Committee Member

University:North Carolina State University

关键词: stone-cech compactification;    topology;    ultrafilter;    hyperreals;   

Others  :  https://repository.lib.ncsu.edu/bitstream/handle/1840.16/5532/etd.pdf?sequence=1&isAllowed=y

美国|英语

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【 摘 要 】

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.