Displaying similar documents to “On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem”

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.

ℳ-rank and meager groups

Ludomir Newelski (1996)

Fundamenta Mathematicae

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Assume p* is a meager type in a superstable theory T. We investigate definability properties of p*-closure. We prove that if T has < 2 ℵ 0 countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.

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...

Near metric properties of function spaces

P. Gartside, E. Reznichenko (2000)

Fundamenta Mathematicae

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"Near metric" properties of the space of continuous real-valued functions on a space X with the compact-open topology or with the topology of pointwise convergence are examined. In particular, it is investigated when these spaces are stratifiable or cometrisable.

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].