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Spring Topology and Dynamical Systems Conference
March 15-17, 2001
Centro de Convenciones
Morelia City, Michoacán, Mexico |
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Organizers
Alejandro Illanes, Sergio Macías, Jesus Muciño, María Luisa Pérez
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On arc-similar and circle-similar continua.
by
Patricia Pellicer
Instituto de Matematicas, Universidad Nacional Autonoma de Mexico.
For a continuum X and p in X, let
C(p, X) = { B in C(X) : p in B }.
A continuum X is arc-similar
if there exist distinct points a, b in X such that
- C(a, X) and C(b, X) are arcs and
- C(p, X) is a 2-cell for all p, except a and b.
On the other hand, X is circle-similar
if C(p, X) is a 2-cell for all p in X.
The following results and characterisations will be presented.
- If X is a decomposable arc-similar continuum, then X is an arc.
- If X is a decomposable circle-similar continuum, then X is a simple closed
curve.
- Proper nondegenerate subcontinua, of a circle-similar continuum are arcs.
Date received: February 8, 2001
Copyright © 2001 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 # cagh-51.