Tightness in Polyadic Spaces.
by
Murray Bell
University of Manitoba, Winnipeg, R3T 2N2, Canada.

Let A_\kappa be the 1-point compactification of the discrete space of cardinality \kappa. A Polyadic space is a Hausdorff image of the space (A_\kappa)^\lambda for some cardinals \kappa and \lambda. We discuss the following unsolved problem: The Gerlits' question whose countable version asks whether every polyadic space of countable tightness is an image of (A_\kappa)^\omega for some cardinal \kappa.
Theorem: A zero-dimensional Polyadic space of countable tightness is a Uniform Eberlein compact space.

Date received: January 28, 2000