How weak is weak extent?
by
Mikhail Matveev
University of California, Davis (Visiting)

The extent of a space X is the cardinal number e(X)=sup{|A|:A is a closed discrete subspace of X}. The weak extent of X is the cardinal number we(X)=min{k: for every open cover U of X there is a subset A of X such that |A| is at most k and St(A, U)=X}. It is easy to see that for every X, we(X) is not greater than e(X). We discuss the question how big can be the difference between e(X) and we(X) for Tychonoff or normal X.

Date received: February 28, 2000

Copyright © 2000 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 # cadv-07.