Keywords and Phrases
"For a metric space X, we denote the hyperspaces of nonempty closed subsets, closed connected subsets, compact subsets, and subcontinua of X by 2X, C(X), K(X), and CK(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 2X, K(X), and CK(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.
Charatonik, W. J.
Roe, Robert Paul
Hilgers, Michael Gene
Mathematics and Statistics
M.S. in Mathematics
University of Missouri--Rolla
v, 17 pages
© 2005 Robbie Allen Beane, All rights reserved.
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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.http://merlin.lib.umsystem.edu/record=b5451572~S5
Beane, Robbie A., "Local compactness of the hyperspace of connected subsets" (2005). Masters Theses. 3721.
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