On a perfect set theorem of A. H. Stone and N. N. Lusin’s constituents

J. Chaber; Gary Gruenhage; Roman Pol

Displaying similar documents to “On a perfect set theorem of A. H. Stone and N. N. Lusin’s constituents”

Selections that characterize topological completeness

Jan van Mill, Jan Pelant, Roman Pol (1996)

Fundamenta Mathematicae

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We show that the assertions of some fundamental selection theorems for lower-semicontinuous maps with completely metrizable range and metrizable domain actually characterize topological completeness of the target space. We also show that certain natural restrictions on the class of the domains change this situation. The results provide in particular answers to questions asked by Engelking, Heath and Michael [3] and Gutev, Nedev, Pelant and Valov [5].

Examples of non-shy sets

Randall Dougherty (1994)

Fundamenta Mathematicae

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Christensen has defined a generalization of the property of being of Haar measure zero to subsets of (abelian) Polish groups which need not be locally compact; a recent paper of Hunt, Sauer, and Yorke defines the same property for Borel subsets of linear spaces, and gives a number of examples and applications. The latter authors use the term “shyness” for this property, and “prevalence” for the complementary property. In the present paper, we construct a number of examples of non-shy...

On regular interstices and selective types in countable arithmetically saturated models of Peano Arithmetic

Teresa Bigorajska, Henryk Kotlarski, James Schmerl (1998)

Fundamenta Mathematicae

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We continue the earlier research of [1]. In particular, we work out a class of regular interstices and show that selective types are realized in regular interstices. We also show that, contrary to the situation above definable elements, the stabilizer of an element inside M(0) whose type is selective need not be maximal.

On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem

Umberto Zannier (1995)

Acta Arithmetica

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Double fibres and double covers: paucity of rational points

J.-L. Colliot-Thélène, A. N. Skorobogatov, Sir Peter Swinnerton-Dyer (1997)

Acta Arithmetica

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The regular open algebra of βRR is not equal to the completion of P(ω)/fin

Alan Dow (1998)

Fundamenta Mathematicae

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Two compact spaces are co-absoluteif their respective regular open algebras are isomorphic (i.e. homeomorphic Gleason covers). We prove that it is consistent that βω and βℝ are not co-absolute.

PCA sets and convexity

R. Kaufman (2000)

Fundamenta Mathematicae

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Three sets occurring in functional analysis are shown to be of class PCA (also called $Σ_{2}^{1}$ ) and to be exactly of that class. The definition of each set is close to the usual objects of modern analysis, but some subtlety causes the sets to have a greater complexity than expected. Recent work in a similar direction is in [1, 2, 10, 11, 12].

Borel extensions of Baire measures

J. Aldaz (1997)

Fundamenta Mathematicae

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We show that in a countably metacompact space, if a Baire measure admits a Borel extension, then it admits a regular Borel extension. We also prove that under the special axiom ♣ there is a Dowker space which is quasi-Mařík but not Mařík, answering a question of H. Ohta and K. Tamano, and under P(c), that there is a Mařík Dowker space, answering a question of W. Adamski. We answer further questions of H. Ohta and K. Tamano by showing that the union of a Mařík space and a compact space...