Functions and Baire spaces
Zbigniew Duszyński (2011)
Kragujevac Journal of Mathematics
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Zbigniew Duszyński (2011)
Kragujevac Journal of Mathematics
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Evans, M.J., Humke, P.D. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Carrese, R., Łazarow, E. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Luis González (1992)
Colloquium Mathematicae
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Luis Bernal-González (1994)
Annales Polonici Mathematici
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We prove some conditions on a complex sequence for the existence of universal functions with respect to sequences of certain derivative and antiderivative operators related to it. These operators are defined on the space of holomorphic functions in a complex domain. Conditions for the equicontinuity of those sequences are also studied. The conditions depend upon the size of the domain.
F. S. De Blasi, G. Pianigiani (1992)
Annales Polonici Mathematici
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An existence theorem for the cauchy problem (*) ẋ ∈ ext F(t,x), x(t₀) = x₀, in banach spaces is proved, under assumptions which exclude compactness. Moreover, a type of density of the solution set of (*) in the solution set of ẋ ∈ f(t,x), x(t₀) = x₀, is established. The results are obtained by using an improved version of the baire category method developed in [8]-[10].
Todorčević, S. (2001)
Bulletin. Classe des Sciences Mathématiques et Naturelles. Sciences Mathématiques
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Péter Komjáth (1995)
Colloquium Mathematicae
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Michał Morayne (1992)
Fundamenta Mathematicae
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We determine the size levels for any function on the hyperspace of an arc as follows. Assume Z is a continuum and consider the following three conditions: 1) Z is a planar AR; 2) cut points of Z have component number two; 3) any true cyclic element of Z contains at most two cut points of Z. Then any size level for an arc satisfies 1)-3) and conversely, if Z satisfies 1)-3), then Z is a diameter level for some arc.
Udayan Darji (1993)
Colloquium Mathematicae
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Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also...
Šalát, T., Tomanová, J. (2007)
Acta Mathematica Universitatis Comenianae. New Series
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