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1
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On compact spaces carrying Radon measures of uncountable Maharam type

100%
Fremlin D. H.
Fundamenta Mathematicae
|
1997
|
tom 154
|
nr 3
295-304
EN
If Martin's Axiom is true and the continuum hypothesis is false, and X is a compact Radon measure space with a non-separable $L^1$ space, then there is a continuous surjection from X onto $[0,1]^{ω_1}$.
2
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Weakly α-favourable measure spaces

100%
Fremlin D. H.
Fundamenta Mathematicae
|
2000
|
tom 165
|
nr 1
67-94
EN
I discuss the properties of α-favourable and weakly α-favourable measure spaces, with remarks on their relations with other classes.
3
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Products of completion regular measures

64%
Fremlin D. H., Grekas S.
Fundamenta Mathematicae
|
1995
|
tom 147
|
nr 1
27-37
EN
We investigate the products of topological measure spaces, discussing conditions under which all open sets will be measurable for the simple completed product measure, and under which the product of completion regular measures will be completion regular. In passing, we describe a new class of spaces on which all completion regular Borel probability measures are τ-additive, and which have other interesting properties.
4
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Universally Kuratowski–Ulam spaces

51%
Fremlin D. H., Natkaniec T., Recław I.
Fundamenta Mathematicae
|
2000
|
tom 165
|
nr 3
239-247
EN
We introduce the notions of Kuratowski-Ulam pairs of topological spaces and universally Kuratowski-Ulam space. A pair (X,Y) of topological spaces is called a Kuratowski-Ulam pair if the Kuratowski-Ulam Theorem holds in X× Y. A space Y is called a universally Kuratowski-Ulam (uK-U) space if (X,Y) is a Kuratowski-Ulam pair for every space X. Obviously, every meager in itself space is uK-U. Moreover, it is known that every space with a countable π-basis is uK-U. We prove the following:  • every dyadic space (in fact, any continuous image of any product of separable metrizable spaces) is uK-U (so there are uK-U Baire spaces which do not have countable π-bases);  • every Baire uK-U space is ccc.
5
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On some properties of Hurewicz, Menger, and Rothberger

45%
Miller A. W., Fremlin D. H.
Fundamenta Mathematicae
|
1988
|
tom 129
|
nr 1
17-33
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