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2 Bulletin of the Polish Academy of Sciences. Mathematics

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Descriptive properties of spaces of measures

Holicky P., Kalenda O.

Bulletin of the Polish Academy of Sciences. Mathematics

1999

Vol. 47, no 1

37-51

The spaces of Borel probabilities on a topological space X inherit a number of topological properties of X. We show in particular that the space of tight probabilities on a Cech-analytic space is Cech-analytic. Analogical results are shown for several other classes of generalized analytic and complete topological spaces.

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.