Local compactness of the hyperspace of connected subsets

Author

Robbie A. Beane

Keywords and Phrases

Buffered continua

Abstract

"For a metric space X, we denote the hyperspaces of nonempty closed subsets, closed connected subsets, compact subsets, and subcontinua of X by 2^X, C(X), K(X), and C_K(X) respectively. In studying hyperspaces it is natural to ask what topological properties the underlying space must possess for a particular hyperspace to have a certain property, and vice-versa. One such topological property is local compactness. There are simple characterizations known for when 2^X, K(X), and C_K(X) are locally compact, but no such characterization exists for C(X).

We formulate a stricter necessary condition and a stricter sufficient condition for local compactness of C(X) than those previously known. We also provide a sufficient condition for metrizability of C(X). In developing these conditions, we introduce the terms buffer and totally buffered. Results relating to buffers and totally buffered spaces are provided, and we propose a characterization of totally buffered continua"--Abstract, page iii.

Advisor(s)

Charatonik, W. J.

Committee Member(s)

Roe, Robert Paul
Hilgers, Michael Gene

Department(s)

Mathematics and Statistics

Degree Name

M.S. in Mathematics

Publisher

University of Missouri--Rolla

Publication Date

Spring 2005

Pagination

v, 17 pages

Note about bibliography

Includes bibliographical references (page 16).

Rights

© 2005 Robbie Allen Beane, All rights reserved.

Document Type

Thesis - Restricted Access

File Type

text

Language

English

Subject Headings

Topology
Continuum (Mathematics)
Hyperspace

Thesis Number

T 8772

Print OCLC #

62775061

Link to Catalog Record

Electronic access to the full-text of this document is restricted to Missouri S&T users. Otherwise, request this publication directly from Missouri S&T Library or contact your local library.

Recommended Citation

Beane, Robbie A., "Local compactness of the hyperspace of connected subsets" (2005). Masters Theses. 3721.
https://scholarsmine.mst.edu/masters_theses/3721