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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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Span and the simple closed curve problem
by
Thelma West
University of Southwestern Louisiana

If X is a non-empty metric space, we define the span \sigma(X) of X to be the least upper bound of the set of real numbers \alpha which satisfy the following condition: There exists a connected space C and continuous mappings f1, f2 : C --> X such that
f1(C) = f2(C)
and
\alpha <= dist[f1(c), f2(c)]
for c in C.

The following question has been asked by Howard Cook.

If S1 and S2 are two simple closed curves in the plane and S2 is contained in the bounded component of R2\S1, then is the span of S1 larger than the span of S2?

In this talk we will discuss this problem and the current partial results.

Date received: March 4, 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-59.