The Stone-Cech Compactification of the Plane

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dc.contributor.advisorGary Faulkner, Committee Chairen_US
dc.contributor.advisorRichard Chandler, Committee Memberen_US
dc.contributor.advisorJesus Rodriguez, Committee Memberen_US
dc.contributor.advisorErnie Stitzinger, Committee Memberen_US
dc.contributor.authorCabbage, Brian Williamen_US
dc.date.accessioned2010-04-02T19:15:23Z
dc.date.available2010-04-02T19:15:23Z
dc.date.issued2006-05-04en_US
dc.degree.disciplineMathematicsen_US
dc.degree.leveldissertationen_US
dc.degree.namePhDen_US
dc.descriptionNorth Carolina State University Theses Mathematics.
dc.description.abstractThe 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.en_US
dc.formatThesis (Ph.D.)--North Carolina State University.
dc.identifier.otheretd-04262006-172615en_US
dc.identifier.urihttp://www.lib.ncsu.edu/resolver/1840.16/5532
dc.rightsI hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.en_US
dc.subjectstone-cech compactificationen_US
dc.subjecttopologyen_US
dc.subjectultrafilteren_US
dc.subjecthyperrealsen_US
dc.titleThe Stone-Cech Compactification of the Planeen_US
dcterms.abstractKeywords: stone-cech compactification, topology, ultrafilter, hyperreals.
dcterms.extentiv, 26 pages : illustrations

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