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dc.contributor.authorEklund, Anthony D.en_US
dc.date.accessioned2014-03-14T21:15:00Z
dc.date.available2014-03-14T21:15:00Z
dc.date.issued1978-05-05en_US
dc.identifier.otheretd-06092012-141053en_US
dc.identifier.urihttp://hdl.handle.net/10919/38597
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_US
dc.format.mediumBTDen_US
dc.publisherVirginia Techen_US
dc.relation.haspartLD5655.V856_1978.E44.pdfen_US
dc.subjectTopologyen_US
dc.subject.lccLD5655.V856 1978.E44en_US
dc.titleThe fine topology and other topologies on C(X,Y)en_US
dc.typeDissertationen_US
dc.contributor.departmentMathematicsen_US
dc.description.degreePh. D.en_US
thesis.degree.namePh. D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen_US
thesis.degree.disciplineMathematicsen_US
dc.contributor.committeechairMcCoy, Robert A.en_US
dc.contributor.committeememberAull, C. E.en_US
dc.contributor.committeememberGreenberg, Williamen_US
dc.contributor.committeememberJohnson, Lee W.en_US
dc.contributor.committeememberParry, Charles J.en_US
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-06092012-141053/en_US
dc.date.sdate2012-06-09en_US
dc.date.rdate2012-06-09
dc.date.adate2012-06-09en_US


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