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dc.contributor.advisorRyden, David James, 1971-
dc.contributor.authorCornelius, Alexander Nelson.
dc.contributor.otherBaylor University. Dept. of Mathematics.en
dc.date.accessioned2009-08-26T10:51:58Z
dc.date.available2009-08-26T10:51:58Z
dc.date.copyright2009-08
dc.date.issued2009-08-26T10:51:58Z
dc.identifier.urihttp://hdl.handle.net/2104/5409
dc.descriptionIncludes bibliographical references (p. 68-69).en
dc.description.abstractMuch is known about inverse limits of compact spaces with continuous bonding maps. When the requirement that the bonding maps be continuous functions is relaxed, to allow for upper semi-continuous set-valued functions, many of the standard tools used to study inverse limit spaces are no longer available. Also, the structure of the inverse limit becomes more complicated. In this dissertation, the structure of compact subsets of the inverse limit is studied. Necessary and sufficient conditions are given for a compact subset of an inverse limit to be the inverse limit of its projections. Weak crossovers are introduced and used to describe the relationship between a set and the inverse limit of its projections. In the process of examining weak crossovers, tools with potentially broader applications are developed. When set-valued bonding maps are continuous and can be written as a union of continuous functions, sufficient conditions to make the inverse limit a Hausdorff continuum are given. It is also shown that, with another assumption, the inverse limit is in fact decomposable. When the bonding map can be written as a union of set-valued functions between compact subsets of the factor space, a description of the inverse limit is given. This uses a generalization of the itinerary of a point.en
dc.description.statementofresponsibilityby Alexander Nelson Cornelius.en
dc.format.extentvii, 69 p. : ill.en
dc.format.extent65247 bytes
dc.format.extent579816 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.language.isoen_USen
dc.rightsBaylor University theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact librarywebmaster@baylor.edu for inquiries about permission.en
dc.subjectSet-valued maps.en
dc.subjectFuntions, Continuous.en
dc.titleInverse limits of set-valued functions.en
dc.typeThesisen
dc.description.degreePh.D.en
dc.rights.accessrightsWorldwide access.en
dc.rights.accessrightsAccess changed 10-31-11.
dc.contributor.departmentMathematics.en


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