Irreducible representations of metrizable spaces and strongly countable-dimensional spaces
Richard Millspaugh, Leonard Rubin, Philip Schapiro (1995)
Fundamenta Mathematicae
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Richard Millspaugh, Leonard Rubin, Philip Schapiro (1995)
Fundamenta Mathematicae
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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].
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.
G. R. Everest, K. Győry (1997)
Acta Arithmetica
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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 countable models then the multiplicity rank ℳ of every type p is finite. We improve Saffe’s conjecture.
L. Lewis Jr. (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...
J.-L. Colliot-Thélène, A. N. Skorobogatov, Sir Peter Swinnerton-Dyer (1997)
Acta Arithmetica
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