On the family of functions with closure of graphs in the Mendez ideals
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Andrzej Nowik
Abstract
We prove some results about additive classes of functions with Lebesgue null or meager closures. We consider also families with closures in the Mendez ideals.
References
[1] Balcerzak, M.—Gła̹b, S.: Measure-category properties of Borel plane sets and Borel functions of two variables, Acta Math. Hungar. 126 (3) (2010), 241–252.10.1007/s10474-009-9055-4Search in Google Scholar
[2] Erdös P.—Kunen, K.—Mauldin, R. D.: Some additive properties of sets of real numbers, Fund. Math. 113 (1981), 187–199.10.4064/fm-113-3-187-199Search in Google Scholar
[3] Grande, Z.—Strońska, E.: Some continuous operations on pairs of cliquish functions, Tatra Mt. Math. Publ. 44 (2009), 15–25.10.2478/v10127-009-0044-3Search in Google Scholar
[4] Kechris, A. S.: Classical Descriptive Set Theory. Graduate Texts in Math. 156, Springer-Verlag, New York, 1995.10.1007/978-1-4612-4190-4Search in Google Scholar
[5] Mendez, C. G.: On sigma-ideals of sets, Proc. Amer. Math. Soc. 60 (1976), 124–128.10.1090/S0002-9939-1976-0417359-8Search in Google Scholar
[6] Mendez, C. G: On the Serpiński-Erdös and the Oxtoby-Ulam theorems for some new sigma-ideals of sets, Proc. Amer. Math. Soc. 72 (1978), 182–188.10.2307/2042560Search in Google Scholar
[7] MAtusik, G.—Natkaniec T.: Algebraic properties of Hamel functions, Acta Math. Hungar. 126 (2010), 209–229.10.1007/s10474-009-9052-7Search in Google Scholar
[8] Srivastava, S. M.: A Course on Borel Sets. Graduate Texts in Math. 180, 1998.10.1007/978-3-642-85473-6Search in Google Scholar
[9] Strońska E.: On the family of functions with a closure of its graph of measure zero, Math. Slovaca 43 (1993), 459–470.Search in Google Scholar
© 2018 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- On the family of functions with closure of graphs in the Mendez ideals
- The predicate completion of a partial information system
- On lattices of z-ideals of function rings
- Compactifications of partial frames via strongly regular ideals
- Lifting components in clean abelian ℓ-groups
- Invariance of nonatomic measures on effect algebras
- On the alexander dual of path ideals of cycle posets
- Generalized multiplicative derivations in 3-prime near rings
- Cleft extensions for quasi-entwining structures
- Groups with positive rank gradient and their actions
- Certain results on q-starlike and q-convex error functions
- Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
- Positive periodic solutions for singular high-order neutral functional differential equations
- A special class of functional equations
- Matrix mappings and general bounded linear operators on the space bv
- Skew-symmetric operators and reflexivity
- Derivatives of Hadamard type in vector optimization
- Cardinal functions of the hyperspace of convergent sequences
- Suzuki-type of common fixed point theorems in fuzzy metric spaces
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Articles in the same Issue
- On the family of functions with closure of graphs in the Mendez ideals
- The predicate completion of a partial information system
- On lattices of z-ideals of function rings
- Compactifications of partial frames via strongly regular ideals
- Lifting components in clean abelian ℓ-groups
- Invariance of nonatomic measures on effect algebras
- On the alexander dual of path ideals of cycle posets
- Generalized multiplicative derivations in 3-prime near rings
- Cleft extensions for quasi-entwining structures
- Groups with positive rank gradient and their actions
- Certain results on q-starlike and q-convex error functions
- Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
- Positive periodic solutions for singular high-order neutral functional differential equations
- A special class of functional equations
- Matrix mappings and general bounded linear operators on the space bv
- Skew-symmetric operators and reflexivity
- Derivatives of Hadamard type in vector optimization
- Cardinal functions of the hyperspace of convergent sequences
- Suzuki-type of common fixed point theorems in fuzzy metric spaces
- Second hankel determinat for certain analytic functions satisfying subordinate condition
