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Spring Topology and Dynamics Conference
March 21-23, 2002
University of Texas
Austin, TX, USA |
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Organizers
Cameron Gordon, John Luecke, Alan Reid
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Z-sets in Hyperspaces
by
Sergio Macias
Institute of Mathematics, National University of Mexico
Coauthors: Sam B. Nadler, Jr. (West Virginia University)
A continuum is a compact connected metric space. Given a
continuum X, the hyperspaces of X that we consider are:
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2X={A subset X | A =/= \emptyset A is closed in\X} |
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Cn(X)={A in 2X | A has at most n components} |
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Fn(X)={A in 2X | A has at most n points}. |
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Illanes and Nadler asked if F1(X) is always a Z-set in
C1(X). We present examples of continua such that F1(X) is
not a Z-set. We also give two classes of continua X such that
Fn(X) is a Z-set in Cn(X)
Date received: January 18, 2002
Copyright © 2002 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Conferences Inc.
Document # caik-06.