Type of Document	Dissertation
Author	Eklund, Anthony D.
URN	etd-06092012-141053
Title	The fine topology and other topologies on C(X,Y).
Degree	PhD
Department	Mathematics
Advisory Committee	Advisor Name Title McCoy, Robert A. Committee Chair Aull, C. E. Committee Member Greenberg, William Committee Member Johnson, Lee W. Committee Member Parry, Charles J. Committee Member
Keywords	Topology
Date of Defense	1978-05-05
Availability	restricted
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.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access  LD5655.V856_1978.E44.pdf 1.81 Mb 00:08:22 00:04:18 00:03:46 00:01:53 00:00:09 next to an author's name indicates that all files or directories associated with their ETD are accessible from the Virginia Tech campus network only.

If you have questions or technical problems, please Contact DLA.