This paper is an exposition of the theory of the hyperspaces 2^X and C(X) of a topological space X. These spaces are obtained from X by collecting the nonempty closed and nonempty closed connected subsets respectively, and are topologized by the Vietoris topology.
The paper is organized in terms of increasing specialization of spaces, beginning with T1 spaces and proceeding through compact spaces, compact metric spaces and metric continua. Several basic techniques in hyperspace theory are discussed, and these techniques are applied to elucidate the topological structure of hyperspaces.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc503983 |
| Date | 12 1900 |
| Creators | Voas, Charles H. |
| Contributors | Lau, Yiu Wa, Hagan, Melvin R. |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 80 leaves : illus, Text |
| Rights | Public, Voas, Charles H., Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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