The fine topology and other topologies on C(X,Y)

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dc.contributor.authorEklund, Anthony D.en
dc.contributor.committeechairMcCoy, Robert A.en
dc.contributor.committeememberAull, Charles E.en
dc.contributor.committeememberGreenberg, Williamen
dc.contributor.committeememberJohnson, Lee W.en
dc.contributor.committeememberParry, Charles J.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:15:00Zen
dc.date.adate2012-06-09en
dc.date.available2014-03-14T21:15:00Zen
dc.date.issued1978-05-05en
dc.date.rdate2012-06-09en
dc.date.sdate2012-06-09en
dc.description.abstract"The Fine Topology" C(X,Y) where (Y,d) is a metric space is referred to, in an exercise in [14], as the topology generated by basic open neighborhoods of the form B(f,E) = {g: d(f(x),g(x)) < E(x)} where E is a positive continuous real valued function. So in the fine topology, a function g is close to f if g(x) is continuously close to f(x); whereas in the uniform topology, g(x) must be uniformly close to f(x), that is, within a constant distance of f(x). So the fine topology is an obvious refinement of the uniform topology. This topology has not been extensively studied before, and it is the purpose of this paper to see how the fine topology fits in with the lattice of other well studied topologies on C(X,Y), and to study some properties of this topology in itself. Furthermore, other results on these well studied topologies will-be examined and compared with the fine topology.en
dc.description.degreePh. D.en
dc.format.extentiv, 44 leaveen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-06092012-141053en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06092012-141053/en
dc.identifier.urihttp://hdl.handle.net/10919/38597en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1978.E44.pdfen
dc.relation.isformatofOCLC# 09227294en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1978.E44en
dc.subject.lcshTopologyen
dc.titleThe fine topology and other topologies on C(X,Y)en
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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