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Abstract  

In the present paper we shall study infinite meet decompositions of an element of a complete lattice. We give here a generalization of some results of papers [2] and [3].

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Abstract  

In 1986, Tong [13] proved that a function f : (X,τ)→(Y,ϕ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A I-sets and A I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, ϕ) is continuous if and only if it is α-I-continuous and A I-continuous.

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. [6] Jain , P. K. , Ahmad , K. 1981 Certain characterisations of Schauder decompositions in Banach spaces Analele Mathematica 19 61 – 66 . [7] Marti , J. T

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means and Riesz decomposition for superbiharmonic functions, Hi-roshima Math. J ., 38 (2008), 231–241. Mizuta Y. Isolated singularities, growth of spherical means and Riesz

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Abstract  

By using m-structures m 1, m 2 on a topological space (X, τ), we define a set D(m 1,m 2) = {A: m 1 Int (A) = m 2 Int (A)} and obtain many decompositions of open sets and weak forms of open sets. Then, the decompositions provide many decompositions of continuity and weak forms of continuity.

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Abstract  

The object of the present paper is to study decomposable weakly conformally symmetric Riemannian manifolds with several non-trivial examples.

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Abstract  

We have introduced α-I-open, semi-I-open and β-I-open sets via idealization and using these sets obtained new decompositions of continuity.

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Acta Mathematica Hungarica
Authors: E. Hatir, E. Hatir, E. Hatir, T. Noiri, T. Noiri, and T. Noiri

Summary  

We introduce the notions of δ-t-sets, δβ-t-sets, δ-B-continuity and δβ -B-continuity and obtain decompositions of continuity and complete continuity.

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Abstract  

A new class of sets in ideal topological spaces is introduced and using these sets, a decomposition of continuity is given.

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Abstract  

We study those functions that can be written as a finite sum of periodic integer valued functions. On ℤ we give three different characterizations of these functions. For this we prove that the existence of a real valued periodic decomposition of a ℤ → ℤ function implies the existence of an integer valued periodic decomposition with the same periods. This result depends on the representation of the greatest common divisor of certain polynomials with integer coefficients as a linear combination of the given polynomials where the coefficients also belong to ℤ[x]. We give an example of an ℤ → {0, 1} function that has a bounded real valued periodic decomposition but does not have a bounded integer valued periodic decomposition with the same periods. It follows that the class of bounded ℤ → ℤ functions has the decomposition property as opposed to the class of bounded ℝ → ℤ functions. If the periods are pairwise commensurable or not prescribed, then we get more general results.

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