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Spring General Topology & Dynamic Systems Conference
March 16-19, 2000
University of the Incarnate Word and The University of Texas at San Antonio
San Antonio, TX, USA |
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Fibrant extensions and conditions of movability
by
Alexander Bykov
Universidad Autónoma de Puebla, México
The concept of a fibrant extension of compacta can be used
in the study of some properties related to different conditions
of movability. For example, ``empty'' strong shape components of
a given compact metric space X, introduced in [1], correspond to
those path components of a fibrant extension Y of X,
which do not intersect X. The fibrant extension Y can be
constructed as a cotelescope of an ANR-sequence associated with X.
Using this representation we prove the following:
If a continuum is movable and virtually pointed 1-movable, then
it is pointed movable.
As a corollary, we get immediately that movable continua, which do not
have ``empty'' strong shape components, are pointed movable. In particular,
continua, both fibrant and movable, are of this kind. In fact, they are
locally path connected approximative polyhedra.
[1] R.Geoghegan, J.Krasinkiewich, Empty components in strong shape theory,
Topology Appl., 41 (1991), 213-233.
Date received: January 27, 2000
Copyright © 2000 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 # cady-16.