On Davenport's bound for the degree of f³ - g² and Riemann's Existence Theorem
Umberto Zannier (1995)
Acta Arithmetica
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Umberto Zannier (1995)
Acta Arithmetica
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J. R. Merriman, S. Siksek, N. P. Smart (1996)
Acta Arithmetica
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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.
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.
J.-L. Colliot-Thélène, A. N. Skorobogatov, Sir Peter Swinnerton-Dyer (1997)
Acta Arithmetica
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Gerald Itzkowitz, Dmitri Shakhmatov (1995)
Fundamenta Mathematicae
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We prove that every nonmetrizable compact connected Abelian group G has a family H of size |G|, the maximal size possible, consisting of proper dense pseudocompact subgroups of G such that H ∩ H'={0} for distinct H,H' ∈ H. An easy example shows that connectedness of G is essential in the above result. In the general case we establish that every nonmetrizable compact Abelian group G has a family H of size |G| consisting of proper dense pseudocompact subgroups of G such that each intersection...
Richard Millspaugh, Leonard Rubin, Philip Schapiro (1995)
Fundamenta Mathematicae
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Paolo De Lucia, Pedro Morales (1998)
Fundamenta Mathematicae
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We present a general decomposition theorem for a positive inner regular finitely additive measure on an orthoalgebra L with values in an ordered topological group G, not necessarily commutative. In the case where L is a Boolean algebra, we establish the uniqueness of such a decomposition. With mild extra hypotheses on G, we extend this Boolean decomposition, preserving the uniqueness, to the case where the measure is order bounded instead of being positive. This last result generalizes...
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].