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Trivial bundles of spaces of probability measures. (Russian) Zbl 0632.46021
For a compact space X, P(X) denotes the space of all regular Borel probability measures on X supplied with the topology \(\sigma (C(X)^*,C(X))\). If Y is another compact space and \(f: X\to Y\) is a continuous mapping then Pf denotes the mapping from PX to PY, induced by f. The main result asserts that for X and Y of finite dimension the following two statements are equivalent:
(1) Pf is a trivial bundle with the Hilbert cube as the fiber;
(2) f is open and all the fibers \(f^{-1}(y)\), \(y\in Y\), are infinite.
Reviewer: S.V.Kislyakov

46E27 Spaces of measures
46M20 Methods of algebraic topology in functional analysis (cohomology, sheaf and bundle theory, etc.)
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