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Spring Topology and Dynamical Systems Conference
March 15-17, 2001
Centro de Convenciones
Morelia City, Michoacán, Mexico

Organizers
Alejandro Illanes, Sergio Macías, Jesus Muciño, María Luisa Pérez

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A fixed point theorem for Whitney blocks
by
Raúl Escobedo
Facultad de Ciencias Físico Matemáticas, B. Universidad Autónoma de Puebla
Coauthors: Jorge Bustamante (Fac. de Ciencias Fís. Mat., BUAP), Fernando Macías-Romero (Fac. de Ciencias Fís. Mat., BUAP)

A continuum is a nonempty compact connected metric space. For a continuum X, let C(X) denote the space of all subcontinua of X with the Hausdorff metric. A Whitney map for C(X) is a continuous function \mu:C(X) --> [0, \infty) such that

  1. \mu({ x}) = 0 for every x in X and

  2. if A, B in C(X) and A subset B =/= A, then \mu(A) < \mu(B).
A Whitney block in C(X) is a set of the form \mu-1([s, t]), where 0 <= s < t <= \mu(X). In this talk we are going to outline the proof of the following result, which answers a question by Sam B. Nadler:

Theorem For a continuum X having zero surjective semispan, each Whitney block in C(X) has the fixed point property.

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-64.