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The property B(P,[alpha])-refinability and its relationship to generalized paracompact topological spaces

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dc.contributor.authorPrice, Ray Hamptonen
dc.contributor.committeechairSmith, James C.en
dc.contributor.committeememberGreen, E.L.en
dc.contributor.committeememberMcCoy, Robert A.en
dc.contributor.committeememberHagedorn, Georgeen
dc.contributor.committeememberArnold, Jesse T.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-08-13T14:38:39Zen
dc.date.available2014-08-13T14:38:39Zen
dc.date.issued1987en
dc.description.abstractThe property B(P,∝)-refinability is studied and is used to obtain new covering characterizations of paracompactness, collectionwise normality, subparacompactness, d-paracompactness, a-normality, mesocompactness, and related concepts. These new characterizations both generalize and unify many well-known results. The property B(P,∝)-refinability is strictly weaker than the property Θ-refinability. A B(P,∝)-refinement is a generalization of a σ-locally finite-closed refinement. Here ∝ is a fixed ordinal which dictates the number of "levels" in a given refinement, and P represents a property such as discreteness or local finiteness which each "level" must satisfy relative to a certain subspace.en
dc.description.adminincomplete_metadataen
dc.description.degreePh. D.en
dc.format.extentiv, 136 leavesen
dc.format.mimetypeapplication/pdfen
dc.identifier.urihttp://hdl.handle.net/10919/49871en
dc.publisherVirginia Polytechnic Institute and State Universityen
dc.relation.isformatofOCLC# 16853178en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1987.P742en
dc.subject.lcshCompact spacesen
dc.subject.lcshCovering spaces (Topology)en
dc.subject.lcshTopological spacesen
dc.titleThe property B(P,[alpha])-refinability and its relationship to generalized paracompact topological spacesen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en

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