dc.contributor.author Eklund, Anthony D. en_US dc.date.accessioned 2014-03-14T21:15:00Z dc.date.available 2014-03-14T21:15:00Z dc.date.issued 1978-05-05 en_US dc.identifier.other etd-06092012-141053 en_US dc.identifier.uri http://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.medium BTD en_US dc.publisher Virginia Tech en_US dc.relation.haspart LD5655.V856_1978.E44.pdf en_US dc.subject Topology en_US dc.subject.lcc LD5655.V856 1978.E44 en_US dc.title The fine topology and other topologies on C(X,Y) en_US dc.type Dissertation en_US dc.contributor.department Mathematics en_US dc.description.degree Ph. D. en_US thesis.degree.name Ph. D. en_US thesis.degree.level doctoral en_US thesis.degree.grantor Virginia Polytechnic Institute and State University en_US thesis.degree.discipline Mathematics en_US dc.contributor.committeechair McCoy, Robert A. en_US dc.contributor.committeemember Aull, C. E. en_US dc.contributor.committeemember Greenberg, William en_US dc.contributor.committeemember Johnson, Lee W. en_US dc.contributor.committeemember Parry, Charles J. en_US dc.identifier.sourceurl http://scholar.lib.vt.edu/theses/available/etd-06092012-141053/ en_US dc.date.sdate 2012-06-09 en_US dc.date.rdate 2012-06-09 dc.date.adate 2012-06-09 en_US
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