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Pseudoarcs, Pseudocircles, Lakes of Wada and generic maps from S2 into R.
by
Udayan B. Darji
University of Louisville
Coauthors: Zoltan Buczolich
Consider the complete metric space C(S2, R), the space of continuous mappings from S2 into R endowed with the supnorm. What is the fiber structure of a generic map? We will show that a generic map has the property that all nondegenerate components of each one of its fibers are figure-eight like and hereditarily indecomposable. Moreover, we will show that pseudoarc, pseudocircles and Lakes of Wada continua appear in abundance as the components of fibers also. The fiber structure of a generic map will be described in a considerable detail. Some results of independent interest in continuum theory and general topology will be proved along the way.
Date received: February 26, 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-68.