Covering Dimension from Large Sets
by
A.H. Stone
Northeastern University

The dimension of a finite-dimensional compact metric space (X, \rho) is the largest n such that, for every finite cover of X by closed sets of diameter at most \epsilon, where \epsilon is sufficiently small, some point of X belongs to more than n of them. How small is sufficient? When X is the unit ball in Euclidean n-space, it is shown that the answer is: \epsilon < 2. For covers by n+1 sets this reduces to a classical theorem about antipodal points on Sⁿ due to Lusternik-Schnirelman and Borsuk.

Date received: April 12, 1996

Copyright © 1996 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 # caaf-81.