Record Details
Uniform convergence on classes of subsets
ScholarsArchive at Oregon State University
| Field | Value |
|---|---|
| Title | Uniform convergence on classes of subsets |
| Names |
Shiflett, Ray Calvin
(creator) Arnold, B. H. (advisor) |
| Date Issued | 1965-12-02 (iso8601) |
| Note | Graduation date: 1966 |
| Abstract | In the study of uniform convergence, one is led naturally to the question of how uniform convergence on subsets relates to uniform convergence on the whole space. This paper develops theorems on how pointwise convergence relates to uniform convergence on finite sets, how uniform convergence on finite subsets relates to uniform convergence on countable sets, and how uniform convergence on countable subsets relates to uniform convergence on uncountable sets. Questions involving uniform convergence on Cauchy sequences are also investigated. These lead to theorems concerning the continuity of limit functions of sequences of continuous functions which converge uniformly on Cauchy sequences. Many of the theorems are generalized ultimately to uniform space. In Chapter III, a topology equivalent to the topology of uniform convergence on compacta on the space of all functions mapping a complete space X to a space Y is introduced. Finally, nets of functions replace sequences of functions, and the possibility of generalizing the previously developed theorems is explored. |
| Genre | Thesis/Dissertation |
| Topic | Convergence |
| Identifier | http://hdl.handle.net/1957/47950 |
