“More or less" first-return recoverable functions.
Evans, M.J., Humke, P.D. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Evans, M.J., Humke, P.D. (2003)
Acta Mathematica Universitatis Comenianae. New Series
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Zbigniew Duszyński (2011)
Kragujevac Journal of Mathematics
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M. Fabian, V. Zizler (2001)
Extracta Mathematicae
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J. Nikiel, L. Treybig (1996)
Colloquium Mathematicae
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Shi, H. (2001)
Acta Mathematica Universitatis Comenianae. New Series
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Ekici, Erdal, Jafari, Saeid (2010)
Acta Universitatis Apulensis. Mathematics - Informatics
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J. Talponen (2007)
Extracta Mathematicae
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J. Cichoń, Michał Morayne (1993)
Fundamenta Mathematicae
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We give an abstract version of Sierpiński's theorem which says that the closure in the uniform convergence topology of the algebra spanned by the sums of lower and upper semicontinuous functions is the class of all Baire 1 functions. Later we show that a natural generalization of Sierpiński's result for the uniform closure of the space of all sums of A and CA functions is not true. Namely we show that the uniform closure of the space of all sums of A and CA functions is a proper subclass...
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].
Plichko, Anatolij (1997)
Serdica Mathematical Journal
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* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95. The main results of the paper are: Theorem 1. Let a Banach space E be decomposed into a direct sum of separable and reflexive subspaces. Then for every Hausdorff locally convex topological vector space Z and for every linear continuous bijective operator T : E → Z, the inverse T^(−1) is a Borel map. Theorem 2. Let us assume the continuum hypothesis....
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.