A Lindelöf separating family over a compact space of uncountable tightness.
by
Oleg Pavlov
Ohio University

Let X be a Tychonoff space and Y subset C_p(X). Then Y separates points of X if for every distinct x₁, x₂ in X there is f in Y such that f(x₁) =/= f(x₂). A. V. Arhangel'skii and V. V. Uspenskii proved that under PFA no compact space of uncountable tightness has a Lindelöf separating family. They asked if this result is true in ZFC. We present a counterexample from diamond. Our example is a perfect continuous preimage of \omega₁+1.

Mailing address: Oleg Pavlov, Ohio University, Department of Mathematics, 321 Morton Hall, Athens, OH, 45701-2979

E-mail address: Oleg.Pavlov@ohiou.edu

Date received: February 25, 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 # caca-51.