Induced universal maps
by
Raúl Escobedo
Facultad de Ciencias Físico Matemáticas, BUAP
Coauthors: María de Jesús López

A continuum is a nonempty, compact, connected, metric space. For a continuum X, let C(X) be the hyperspace of all subcontinua of X, with the Hausdorff metric. A map between continua, f:X --> Y , induces a map between their hyperspaces, [^f]:C(X) --> C(Y) , defined by [^f](A) = f(A) , for each A in C(X) .

The map f is said to be universal provided that, for each map g\colon X --> Y , there exists a point p in X such that f(p) = g(p) . A continuum Y is said to be in Class(U) (Class([^U]), Class(W), respectively), if for every map from any continuum X onto Y, f\colon X --> Y, it holds that f is universal ([^f] is universal, [^f] is onto, respectively). In this talk we point out some connections between these classes of continua and sketch the proof of the following result:

Theorem. A circle-like continuum X is in Class([^U]) if and only if X is in Class(W).

Date received: February 27, 2003

Copyright © 2003 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 # cajz-81.