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New examples of hereditarily t-Baire spaces

Kalenda O.

Bulletin of the Polish Academy of Sciences. Mathematics

1998

Vol. 46, no 2

197-210

We introduce a new class of hereditarily t-Baire spaces (defined by G. Koumoullis (1993) - see below) which need not to have the restricted Baire property in a compactification - as an example serves the space (O,omega[sup 1])^A for A uncountable. We use this and a modification of a construction of D. Fremlin (1987) to get, under the assumption that there is a measurable cardinal, an example of a first class function of a hereditarily t-Baire space into a metric space which has no point of continuity, which shows, in answer to a question of G. Koumoullis (1993), that the cardinality restriction in his Theorem 4.1 cannot be dropped.