Á. Császár

Eötvös Loránd University, Budapeŝto, Budapest, Hungary

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Publications (52)22.47 Total impact

  • Ákos Császár
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    ABSTRACT: We define weak structures and show that these structures can replace in many situations generalized topologies or minimal structures.
    Acta Mathematica Hungarica 01/2011; 131(1):193-195. DOI:10.1007/s10474-010-0020-z · 0.40 Impact Factor
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    Á. Császár · E. Makai Jr
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    ABSTRACT: In generalizing constructions of N.V. Veličko, the paper starts from two generalized topologies µ and µ′ on a set X and introduces two more generalized topologies gd(µ, µ′) and δ(µ,µ′) with the examination of their properties.
    Acta Mathematica Hungarica 05/2009; 123(3). DOI:10.1007/s10474-009-8088-z · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: The definition of the product of topologies is generalized in such a way that topologies are replaced by generalized topologies in the sense of [3].
    Acta Mathematica Hungarica 01/2009; 123(1):127-132. DOI:10.1007/s10474-008-8074-x · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: As generalization of the construction of I-τ where τ is a topology and I is an ideal [11], and similarly of $$ \mathcal{H} $$-µ where µ is a generalized topology and $$ \mathcal{H} $$ is a hereditary class [5], we introduce generalized topologies starting from two generalized topologies µ and µ′.
    Acta Mathematica Hungarica 01/2009; 122(1):153-159. DOI:10.1007/s10474-008-8002-0 · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: It is shown in the paper [1] that every generalized topology can be generated by a generalized neighbourhood system. Following the paper [3], we discuss some questions related to this construction.
    Acta Mathematica Hungarica 12/2008; 121(4). DOI:10.1007/s10474-008-7224-5 · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: The paper discusses the generalization of a construction described in [6] for the case when the starting point topology is replaced by a generalized topology.
    Acta Mathematica Hungarica 09/2008; 120(4):351-354. DOI:10.1007/s10474-008-7115-9 · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: It is shown that the theory of δ-and θ-modifications of topological spaces (see [3]) can be generalized for the case when the topology is replaced by a generalized topology in the sense of [1].
    Acta Mathematica Hungarica 07/2008; 120(3):275-279. DOI:10.1007/s10474-007-7136-9 · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: A quasi-topology is a generalized topology (cf. [3]) closed for finite intersections. The paper discusses the question whether statements valid for topologies can be generalized for quasi-topologies.
    Acta Mathematica Hungarica 04/2008; 119(1):197-200. DOI:10.1007/s10474-007-7023-4 · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: The concept of normality is defined for generalized topologies in the sense of [1], a few properties of normal spaces are proved, and their characterization with the help of a suitable form of Urysohn’s lemma is discussed.
    Acta Mathematica Hungarica 06/2007; 115(4):309-313. DOI:10.1007/s10474-007-5249-9 · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: The purpose of the paper is to show that the construction leading from a topology and an ideal of sets to another topology remains valid, together with a lot of applications, if topology is replaced by generalized topology and ideal by hereditary class.
    Acta Mathematica Hungarica 03/2007; 115(1):29-36. DOI:10.1007/s10474-006-0531-9 · 0.40 Impact Factor
  • Ákos Császár
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    ABSTRACT: Summary There is a formula for the interior of a set in a generalized topology composed of the γ-open sets, where γ is a monotonic map in the power set of X. There are known conditions for a γ assuring that this formula is valid. The paper gives essential generalizations for these conditions and contains some applications.
    Acta Mathematica Hungarica 10/2006; 113(4):325-332. DOI:10.1007/s10474-006-0109-6 · 0.40 Impact Factor
  • Ákos Császár
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    ABSTRACT: It is proved a rather general version of the statement that if the union of arbitrary elements of a system λ always belongs to λ then the intersections of elements of λ constitute an ultratopology (i.e. a topology where intersections of open sets are open).
    Acta Mathematica Hungarica 12/2005; 110(1):153-157. DOI:10.1007/s10474-006-0011-2 · 0.40 Impact Factor
  • Ákos Császár
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    ABSTRACT: Summary In the paper [5], several operations on generalized topologies are considered. They are not monotone in general, but an old result on monotonicity may be sharpened.
    Acta Mathematica Hungarica 08/2005; 108(4):351-354. DOI:10.1007/s10474-005-0230-y · 0.40 Impact Factor
  • Ákos Császár
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    ABSTRACT: Summary We study the even power means of a sum analogous to Dedekind sums, and give a sharp asymptotic formula.
    Acta Mathematica Hungarica 01/2005; 106(1):53-66. DOI:10.1007/s10474-005-0005-5 · 0.40 Impact Factor
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    Ákos Császár
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    ABSTRACT: The paper presents a formula for the γ-interior of a set under special conditions for γ:expX→expX, more general than those in the previous paper [Acta Math. Hungar. 80 (1998) 89–93]. There are also some applications.
    Journal of Mathematical Analysis and Applications 09/2004; 297(2):490-494. DOI:10.1016/j.jmaa.2004.03.071 · 1.12 Impact Factor
  • Ákos Császár
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    ABSTRACT: The fundamental concepts in topological spaces, in particular separation axioms, are presented in a manner that open sets are replaced by more general ones.
    Acta Mathematica Hungarica 06/2004; 104(1):63-69. DOI:10.1023/B:AMHU.0000034362.97008.c6 · 0.40 Impact Factor
  • Ákos Császár
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    ABSTRACT: The investigations in [3] are made more precise by considering not only separation axioms for topological spaces but also those connected with Čech closures.
    Acta Mathematica Hungarica 01/2004; 102(3):249-260. DOI:10.1023/B:AMHU.0000023220.74326.3f · 0.40 Impact Factor
  • Ákos Császár
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    ABSTRACT: The author examines separation properties of the modification () of a topology connected with the concept of -cluster points in the sense of N. V. Veliko.
    Acta Mathematica Hungarica 12/2003; 102(1):151-158. DOI:10.1023/B:AMHU.0000023213.27928.02 · 0.40 Impact Factor
  • Á. Császár
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    ABSTRACT: It is shown that the concept of a connected set and the essential properties of connected sets can be generalized in the manner that the role of open sets is given to γ-open sets, where γ is a monotonic mapping of the power set.
    Acta Mathematica Hungarica 12/2003; 101(4):273-279. DOI:10.1023/B:AMHU.0000004939.57085.9e · 0.40 Impact Factor
  • Á Császár
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    ABSTRACT: The purpose of the paper is to present some kind of characterization for coarsest or finest elements in a subcategory of MER that induce an element of another given subcategory.
    Acta Mathematica Hungarica 01/2003; 98(1):9-19. DOI:10.1023/A:1022845002637 · 0.40 Impact Factor

Publication Stats

558 Citations
22.47 Total Impact Points

Institutions

  • 1994–2011
    • Eötvös Loránd University
      • Department of Analysis
      Budapeŝto, Budapest, Hungary