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II Congreso Iberoamericano de Topología y sus Aplicaciones
March 20-22, 1997

Morelía, Mexico

Organizers
Salvador García-Ferreira, Daniel Juan Pineda, Sergio Macías Alvarez, Max Neumann Coto, María L. Pérez Seguí, Salvador Romaguera Bonilla, Manuel Sanchis López, Angel Tamariz Mascarúa, M. G. Tkachenko, Javier F. Trigos Arrieta

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Limit properties of induced mappings
by
Janusz J. Charatonik
University of Wroclaw and Universidad Nacional Autónoma de México
Coauthors: Wlodzimierz J. Charatonik

Given a class M of mappings f : X --> Y between continua X and Y, we denote by near-M the class of uniform limits of sequences of mappings belonging to M. Let 2f : 2X --> 2Y and C(f) : C(X) --> C(Y) be the induced mappings between hyperspaces. Relations are studied between the conditions: f in near-M, 2f in near-M, and C(f) in near-M. Special attention is paid to the class M of homeomorphisms and of open mappings. It is proved that if the mapping f is monotone, then the induced mappings 2f and C(f) are cell-like. As an application examples of mappings are constructed such that:

  1. 2f and C(f) are near-homeomorphisms, while f is not;

  2. 2f is a near-homeomorphism, while f and C(f) are not;

  3. f is open and C(f) is not near-open;

  4. 2f and C(f) are near-homeomorphisms, while f is not near-open.

Date received: February 9, 1997

Copyright © 1997 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 # caak-09.