I share my impressions from Nagata’s work and from his person. To me he represents a monumental figure in the history of General Topology in the second half of twentieth century.

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The article concerns the influence of one Nagata’s idea with the dimension theory of general topological spaces. The addition to the article contains proofs of very general sufficient conditions for the Ind-product theorem (for Tychonoff products) and for the Ind-subset theorem (which were published without proofs earlier).

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In this paper, we first introduce the notion of closed filters in CI-algebras. Next we provide some properties of closed filters. Finally we investigate how to generate a closed filter by a subset in a transitive CI-algebra.

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In this article, we summarize the late J. Nagata’s contribution to the theory of generalized metric spaces. Especially, the central point of our discussion we give here is the so-called Nagata-Smirnov’s metrization theorem and its application. We state how he has influenced us in this field.

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Using fuzzy filters in the sense of P. Eklund and W. G¨ahler [2] in fuzzy preuniform convergence spaces as introduced in [11] compactness and weak compactness are presented by means of convergence and preconvergence of fuzzy ultrafilters respectively. The generalization of these concepts by localization leads to bicoreflective subconstructs of the construct of FPUConv of fuzzy preuniform convergence spaces which are additionally cartesian closed. These results are even new in the non-fuzzy case (i.e. in the realm of preuniform convergence spaces) which is included and improve the situation for topological spaces.

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Conjoint analysis is a scaling method originally developed in mathematical psychology. Today it is used in many of the social sciences and applied sciences including marketing, product management, and operations research. It is used for measuring each factorfs contribution to the whole evaluation of products consisting of some factors, for example, in testing customer acceptance of new product designs, in assessing the appeal of advertisements and in service design. TRADE-OFF is a method of conjoint analysis used for measuring the part worth value of factors in the total evaluation, exclusively using when evaluations is non-metrical data. The part worth values obtained by TRADE-OFF give an approximate comparison of each factor’s contribution to the total evaluation, but it is impossible to utilize their contributions for statistical use since they are usually obtained by numerical solution. Moreover, their solution isn’t correct and unique. And it is known that the part worth value obtained by In this paper, we show the problems of TRADE-OFF and then propose a method to obtain its definite solution.

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In this manuscript, we classify non isomorphic quasi union hyper Kalgebras of order 6 and show that conjecture 4.2[6] is not true generally, and finally modify it.

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We determine support points of the subordination family of an arbitrary bounded analyltic function, thereby proving the Abu-Muhanna conjecture [J. London Math. Soc. (2), 29 (1984)].

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The major objective of this article is a refinement of treatments of the mutual relationship between two notions of “sequential computability” of a function which is possibly Euclidean-discontinuous, one using limiting recursion and one using effective uniformity. We also speculate on these methods from a mathematician’s viewpoint.

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In this note we introduce a function space, which is used to define kernels of singular integrals. The space is useful in proving Lp boundedness of certain singular integrals via extrapolation arguments under a sharp condition on their kernels.

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In this paper we introduce the notion of derivation of incline algebras, and we prove some result on derivation of an incline and integral incline. Moreover, we show that if a derivation is nonzero on an integral incline K , then it is nonzero on any nonzero ideal of K.

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The purpose of this paper is to study the characterization of a Hermite’s interpolation formula to produce the generalized quotient and remainder theorem of polynomials and its formulae.

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In this paper, we first introduce the notion of closed filters in CI-algebras. Next we provide some properties of closed filters. Finally we investigate how to generate a closed filter by a subset in a transitive CI-algebra.

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