Quasi-sums in several variables.
Maksa, Gyula, Nizsalóczki, Enikő (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Maksa, Gyula, Nizsalóczki, Enikő (2006)
Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]
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Janusz Pawlikowski, Ireneusz Recław (1995)
Fundamenta Mathematicae
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We parametrize Cichoń’s diagram and show how cardinals from Cichoń’s diagram yield classes of small sets of reals. For instance, we show that there exist subsets N and M of and continuous functions such that • N is and , the collection of all vertical sections of N, is a basis for the ideal of measure zero subsets of ; • M is and is a basis for the ideal of meager subsets of ; •. From this we derive that for a separable metric space X, •if for all Borel (resp. ) sets...
Ramez Sami (1999)
Fundamenta Mathematicae
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We prove the following theorem: Given a⊆ω and , if for some and all u ∈ WO of length η, a is , then a is . We use this result to give a new, forcing-free, proof of Leo Harrington’s theorem: -Turing-determinacy implies the existence of .
Krzysztof Frączek (2000)
Fundamenta Mathematicae
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We study ergodicity of cylinder flows of the form , , where is a measurable cocycle with zero integral. We show a new class of smooth ergodic cocycles. Let k be a natural number and let f be a function such that is piecewise absolutely continuous (but not continuous) with zero sum of jumps. We show that if the points of discontinuity of have some good properties, then is ergodic. Moreover, there exists such that if is a function with zero integral such that is of bounded...
Gurucharan Singh Saluja (2011)
Kragujevac Journal of Mathematics
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Boban Veličković (1999)
Fundamenta Mathematicae
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Using Tsirelson’s well-known example of a Banach space which does not contain a copy of or , for p ≥ 1, we construct a simple Borel ideal such that the Borel cardinalities of the quotient spaces and are incomparable, where is the summable ideal of all sets A ⊆ ℕ such that . This disproves a “trichotomy” conjecture for Borel ideals proposed by Kechris and Mazur.
Michael Levin (1995)
Fundamenta Mathematicae
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Let X be a compactum and let be a countable family of pairs of disjoint subsets of X. Then A is said to be essential on Y ⊂ X if for every closed separating and the intersection is not empty. So A is inessential on Y if there exist closed separating and such that does not intersect Y. Properties of inessentiality are studied and applied to prove: Theorem. For every countable family of pairs of disjoint open subsets of a compactum X there exists an open set G ∩ X on...
Michael Levin (1996)
Fundamenta Mathematicae
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Let X and Y be compacta and let f:X → Y be a k-dimensional map. In [5] Pasynkov stated that if Y is finite-dimensional then there exists a map such that dim (f × g) = 0. The problem that we deal with in this note is whether or not the restriction on the dimension of Y in the Pasynkov theorem can be omitted. This problem is still open. Without assuming that Y is finite-dimensional Sternfeld [6] proved that there exists a map such that dim (f × g) = 1. We improve this result of Sternfeld...
Martin Helm (1993)
Acta Arithmetica
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Introduction. An old conjecture of P. Erdős repeated many times with a prize offer states that the counting function A(n) of a -sequence A satisfies . The conjecture was proved for r=2 by P. Erdős himself (see [5]) and in the cases r=4 and r=6 by J. C. M. Nash in [4] and by Xing-De Jia in [2] respectively. A very interesting proof of the conjecture in the case of all even r=2k by Xing-De Jia is to appear in the Journal of Number Theory [3]. Here we present a different, very short proof...
S. Srivastava (1995)
Fundamenta Mathematicae
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We prove the existence of Carathéodory selections and representations of a closed convex valued, lower Carathéodory multifunction from a set A in into a separable Banach space Y, where ℰ is a sub-σ-field of the Borel σ-field ℬ(E) of a Polish space E, X is a Polish space and A is the Suslin operation. As applications we obtain random versions of results on extensions of continuous functions and fixed points of multifunctions. Such results are useful in the study of random differential...
Marín, Josefa, Romaguera, Salvador (1991)
Commentationes Mathematicae Universitatis Carolinae
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Martin Arkowitz, Marek Golasiński (1994)
Fundamenta Mathematicae
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Let G be a finite group, the category of canonical orbits of G and b a contravariant functor to the category of abelian groups. We investigate the set of G-homotopy classes of comultiplications of a Moore G-space of type (A,n) where n ≥ 2 and prove that if such a Moore G-space X is a cogroup, then it has a unique comultiplication if dim X < 2n - 1. If dim X = 2n-1, then the set of comultiplications of X is in one-one correspondence with . Then the case leads to an example of...