Characteristics of Complexity within the Lattice of Compactifications

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dc.contributor.advisor Dr. Ernest Stitzinger, Committee Member en_US
dc.contributor.advisor Dr. William Swallow, Committee Member en_US
dc.contributor.advisor Dr. Gary D. Faulkner, Committee Chair en_US
dc.contributor.advisor Dr. Richard Chandler, Committee Member en_US
dc.contributor.advisor Dr. Jo-Ann Cohen, Committee Member en_US Mawhinney, Katherine Joyner en_US 2010-04-02T18:51:44Z 2010-04-02T18:51:44Z 2003-07-07 en_US
dc.identifier.other etd-04032003-133822 en_US
dc.description.abstract The purpose of this research is to determine some topological characteristics that may be used to classify a Hausdorff compactification of a topological space as a complex compactification, within the lattice of compactifications. The Stone-Cech compactification is the supremum of the lattice, the Alexandroff one-point compactification the infimum. We look to characteristics that the Stone-Cech compactification holds and whether or not those properties are found in compactifications "close" to it. The idea of a complex compactification has not been strictly defined and there are numerous properties that could be used in a definition. Beginning with mappings with a finite number of nontrivial fibers,, we find that F-space is invariant. F-space can not be guaranteed for all finite-to-one mappings. The characteristic we call G-int under any finite-to-one irreducible mapping and the continuous image of a nowhere F space is nowhere F, a characteristic of compactifications that are simple. We also consider the mappings on the Stone-Cech compactification of the natural numbers that are simple mappings, proving that if a simple mapping is finite-to-one, then so is its generator and vice versa. en_US
dc.rights I 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.subject compactifications en_US
dc.subject Stone-Cech en_US
dc.subject Parovicenko spaces en_US
dc.title Characteristics of Complexity within the Lattice of Compactifications en_US PhD en_US dissertation en_US Mathematics en_US

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