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Start Over Author "Pol R" Journal transactions of the american mathematical society
4 results on '"Pol R"'

3. ON BOREL MAPS, CALIBRATED s-IDEALS, AND HOMOGENEITY.

Author

POL, R. and ZAKRZEWSKI, P.

Subjects
*BOREL subgroups, *MATHEMATICAL analysis, *LATTICE theory, *MATHEMATICS theorems, *ALGEBRA
Abstract

Let μ be a Borel measure on a compactum X. The main objects in this paper are s-ideals Ipdimq, J0pμq, Jf pμq of Borel sets in X that can be covered by countably many compacta which are finite-dimensional, or of μ-measure null, or of finite μ-measure, respectively. Answering a question of J. Zapletal, we shall show that for the Hilbert cube, the s-ideal Ipdimq is not homogeneous in a strong way. We shall also show that in some natural instances of measures μ with nonhomogeneous s-ideals J0pμq or Jf pμq, the completions of the quotient Boolean algebras BorelpXq{J0pμq or BorelpXq{Jf pμq may be homogeneous. We discuss the topic in a more general setting, involving calibrated s-ideals. [ABSTRACT FROM AUTHOR]

Published
2018
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4. Descriptive complexity of function spaces

Author

Lutzer, D., Mill, J. van, and Pol, R.

Abstract

In this paper we show that $ {C_\pi }(X)$ topologized by the pointwise convergence topology, can have arbitrarily high Borel or projective complexity in $ {{\mathbf{R}}^X}$ is a countable regular space with a unique limit point. In addition we show how to construct countable regular spaces $ X$ $ {C_\pi }(X)$ "$.

Published
1985

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