Results 1 to 10 of about 37 (37)
Haar null and Haar meager sets: a survey and new results
Bulletin of the London Mathematical Society, Volume 52, Issue 4, Page 561-619, August 2020., 2020 Abstract We survey results about Haar null subsets of (not necessarily locally compact) Polish groups. The aim of this paper is to collect the fundamental properties of the various possible definitions of Haar null sets, and also to review the techniques that may enable the reader to prove results in this area.
Márton Elekes, Donát Nagy
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A dichotomy of sets via typical differentiability
Forum of Mathematics, Sigma, 2020 We obtain a criterion for an analytic subset of a Euclidean space to contain points of differentiability of a typical Lipschitz function: namely, that it cannot be covered by countably many sets, each of which is closed and purely unrectifiable (has a ...
Michael Dymond, Olga Maleva
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Separating sets by bilaterally quasi-continuous functions [PDF]
, 2021 In this paper we characterize the pairs (A0;A1) and (A-, A+) of disjoint sets which can be separated by a bilaterally quasi-continuous function. Moreover, we characterize when two arbitrary subsets of the real line can be separated by bilaterally dense ...
Syzsykowska, Paulina
core
Nikolai Luzin and the problem of existence in mathematics
Revista Integración, 2017 This paper presents excerpts of the discussion about the problem of existence for functions in each one of Baire’ s classes. First, it sets up the historical problem, introducing four existential categories, and then it shows Luzin’ s position and ...
Andrés Chaves, Luis C. Recalde
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On functions determined by limit sets and the quasi-Świątkowski property [PDF]
, 2021 We introduce and investigate the class of functions determined by limit sets for which at each point the intersection of the sets of left-hand and right-hand limit numbers is singleton containing value of function at this point.
Chmielewska, Kataryzna +1 more
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Prevalence of backward stochastic differential equations with unique solution
International Journal of Stochastic Analysis, Volume 2004, Issue 2, Page 123-136, 2004., 2004 We prove that in the sense of Baire category, almost all backward stochastic differential equations (BSDEs) with bounded and continuous coefficient have the properties of existence and uniqueness of solutions as well as the continuous dependence of solutions on the coefficient and the L2‐convergence of their associated successive approximations.
K. Bahlali, B. Mezerdi, Y. Ouknine
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On common fixed points, periodic points, and recurrent points of continuous functions
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 39, Page 2465-2473, 2003., 2003 It is known that two commuting continuous functions on an interval need not have a common fixed point. However, it is not known if such two functions have a common periodic point. we had conjectured that two commuting continuous functions on an interval will typically have disjoint sets of periodic points.
Aliasghar Alikhani-Koopaei
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Note on limits of simply continuous and cliquish functions
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 447-450, 1994., 1993 The main result of this paper is that any function f defined on a perfect Baire space (X, T) with values in a separable metric space Y is cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence {fn : n ≥ 1} of simply continuous functions. This result is obtained by a change of a topology on X and showing that a function f : (
Janina Ewert
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Diagonals of separately continuous maps with values in box products
Topological Algebra and its Applications, 2018 We prove that if X is a paracompact connected space and Z = ∏s∈S Zs is a product of a family of equiconnected metrizable spaces endowed with the box topology, then for every Baire-one map g : X → Z there exists a separately continuous map f : X2 → Z such
Karlova Olena, Mykhaylyuk Volodymyr
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Separating sets in bitopological spaces by P-LSC and L-USC functions [PDF]
, 2019 In this paper we characterize the pairs ⟨A0,A1⟩ and ⟨A- ,A+⟩ of dis- joint subsets of bitopological space (X, P, L) which can be separated by the function f : X → R simultaneously lower semicontinuous in the topology P and upper semi-continuous in the ...
Szyszkowska, Paulina
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