Concerning ordered spaces

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dc.contributor.advisorIngram, William T.
dc.contributor.committeeMemberYounglove, James N.
dc.contributor.committeeMemberKnopp, Paul J.
dc.contributor.committeeMemberHoward, Wendell T.
dc.creatorOberhoff, Kenneth E.
dc.date.accessioned2022-02-03T16:56:44Z
dc.date.available2022-02-03T16:56:44Z
dc.date.issued1968
dc.description.abstractOrdered spaces are an abstraction of the real line. This paper shows in Chapter 1 that all ordered spaces are hereditarily normal. In Chapter 2, necessary and sufficient conditions are given for a separable ordered space to be completely separable, and hence metrizable. In semi-metrizable ordered spaces the following are shown to be equivalent: (a) The space is completely separable. (b) The space is separable. (c) The space is hereditarily separable. (d) The space has the Lindelof property. (e) If M is an uncountable subset of the space, then some point of M is a limit point of M. (f) There does not exist an uncountable collection of mutually exclusive open sets in the space.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other13678583
dc.identifier.urihttps://hdl.handle.net/10657/8649
dc.language.isoen
dc.rightsThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. §107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.
dc.titleConcerning ordered spaces
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Arts and Sciences
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelMasters
thesis.degree.nameMaster of Science

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