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The 12th Summer Conference on General Topology and its Applications
August 12-16, 1997
Nipissing University
North Bay, ON, Canada

Organizers
Ted Chase, Boguslaw Schreyer, Jodi Sutherland, Murat Tuncali, Stephen Watson

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Approximation with Bing Maps
by
Jianwei Song
University of Saskatchewan
Coauthors: E. D. Tymchatyn

A Bing space is a metric compactum such that all of its subcontinua are hereditarily indecomposable. A map is a Bing map if its fibers are Bing spaces. A space Y is free if for every continuum X the set of Bing maps from X to Y is dense in C(X, Y). M.Levin proved that the unit interval is free and Jozef Krasinkiewicz showed that n-manifolds (n >= 1) are free.

We answered some questions of Krasinkiewicz by proving the following:

Theorem : Let Y be a ANR space. If Y is locally free, then Y is a free space.

Theorem : Every graph with non-degenerate components is a free space.

Collorary : Every 1-dimensional Peano continuum is a free space.

Date received: June 23, 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 # caao-15.