Zero span continua

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dc.contributor.advisorIngram, William T.
dc.contributor.committeeMemberCook, Howard
dc.contributor.committeeMemberLelek, Andrew S.
dc.contributor.committeeMemberBrown, Dennison R.
dc.contributor.committeeMemberBenbrook, Joyce
dc.creatorDavis, James Francis, 1870-1942
dc.date.accessioned2024-01-02T20:06:10Z
dc.date.available2024-01-02T20:06:10Z
dc.date.issued1981
dc.description.abstractThis dissertation is concerned with the span of continua and with continua in class W. The emphasis of this study is on the class of continua which have zero span. The relationship between this class and class W is studied. The author introduces in this dissertation the notion of the symmetric span of a continuum by modifying Lelek's origional definition. Continua with zero span have zero symmetric span but the converse does not hold. The author proves that the continua with zero symmetric span are in class W. Lelek defined the semispan of a continuum M by relaxing a condition in the definition of span. Lelek gives an example of a continuum for which the span and semispan are different. The author shows that if every subcontinuum of the continuum M is in class W, then the span and semispan of M are the same. This result and the previous one are then applied to show that the span of a continuum is zero if and only if the semispan is zero. This has the corollary that continua with zero span have the fixed point property. A second corollary of this theorem generalizes a recent result of Duda and Kell to the following: If H and K are continua with zero span which intersect, H n K is connected, and H u K is atriodic then H u K has zero span. Next, decomposable, atriodic continua are studied. After preliminary lemmas. It is shown that if H and K are continua in class W which intersect, H n K is connected, and H u K is atriodic then H u K is in class W. Finally certain homogeneous continua are studied. It is shown that homogeneous, almost chainable continua have zero span.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
dc.format.mimetypeapplication/pdf
dc.identifier.other8608618
dc.identifier.urihttps://hdl.handle.net/10657/15719
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. Section 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.subjectMetric spaces
dc.subjectContinuity
dc.titleZero span continua
dc.type.dcmiText
dc.type.genreThesis
thesis.degree.collegeCollege of Natural Sciences and Mathematics
thesis.degree.departmentMathematics, Department of
thesis.degree.disciplineMathematics
thesis.degree.grantorUniversity of Houston
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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