Pseudocompactness of hyperspaces
by
Michael Hrusak
UNAM, Mexico
Coauthors: Fernando Hernandez and Ivan Martinez

A question of J. Ginsburg asks: Is there any relationship between the pseudocompactness of X^w and that of the hyperspace 2^X? We consider the question in general and also in the context of Y-spaces.

While the space Y(A)^w is pseudocompact for every MAD family A, it is undecidible in ZFC whether 2^Y(A) is. We show that

1) (p = c) 2^Y(A) is pseudocompact for every MAD family A.

2) (h < non(meagre)) There is a MAD family A such that 2^Y(A) is not pseudocompact.

3) We construct a ZFC example of a space X such that X^w is pseudocompact but 2^X is not.

Date received: February 28, 2006