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Continuous selections with respect to extension dimension
by
A. V. Karasev
University of Saskatchewan
Let L be a finite CW complex. By [L] we denote extension type of L. The following generalization of Michael's selection theorem is proved:
Theorem Consider [L] £ [Sn]. Let F be a lower semi-continuous map between polish space X and metrizable compactum Y, such that ed (X) £ [L] (where ed (X) denotes an extension dimension of X, F is equi-LC[L] collection and F(x) Î AE ([L]) for any x Î X. Let A be a closed subset of X such that there exists a continuous selection f:A ® Y of F|A. Then F admits a continuous selection f¢ which extends f.
Paper reference: arXiv:math.GN/9912193
Date received: December 22, 1999
Copyright © 1999 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 # cady-02.