Concerning the cone = hyperspace property

dc.contributor.advisorIngram, William T.
dc.contributor.committeeMemberBrown, Dennison R.
dc.contributor.committeeMemberCook, Howard
dc.contributor.committeeMemberLelek, Andrew S.
dc.contributor.committeeMemberWheeler, Lewis T.
dc.creatorMarsh, Dorothy Sherling
dc.description.abstractAn example of a one-dimensional, nonchainable, noncircle-like continuum is constructed and shown to have the cone = hyperspace property. In addition, it is proved that a sufficient condition for a continuum X to have the cone = hyperspace property is that there exists a selection for C(X){X} which, for some Whitney map for C(X) , maps each nondegenerate Whitney level homeomorphically onto X . The class of Whitney stable continua includes the arc, the circle, the pseudo-arc, and the solenoids. It is shown that a certain example due to W. T. Ingram of a nonchainable, atriodic, tree-like continuum is also Whitney stable.
dc.description.departmentMathematics, Department of
dc.format.digitalOriginreformatted digital
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dc.titleConcerning the cone = hyperspace property
dcterms.accessRightsThe full text of this item is not available at this time because it contains documents that are presumed to be under copyright and are accessible only to users who have an active CougarNet ID. This item will continue to be made available through interlibrary loan. of Natural Sciences and Mathematics, Department of of Houston of Philosophy


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