Real and Complex Analysis

On fuzzy semicontinuity, fuzzy almost continuity and fuzzy weakly continuity

The paper defines, with the help of generalized topologies and generalized neighbourhood systems, two kinds of generalized continuity, by giving in this way a general form to various concepts discussed in the literature. In particular, generalized continuity admits a characterization furnishing a known charcterization of θ-continuous maps.

Generalized topology, generized continuity

Generalized Open Sets

In 1982 and 1970, Hdeib and Levine introduced the notions of ω-closed set and generalized closed set, respectively. The aim of this paper is to provide a relatively new notion of generalized closed set, namely, regular generalized ω-closed, regular generalized ω-continuous, a-ω-continuous, and regular generalized ω-irresolute maps and to study its fundamental properties.

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Regular generalized ω-closed sets

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.

On decompositions of continuity via idealization

In Hatir and Noiri [Hatir E, Noiri T. Decompositions of continuity and complete continuity. Acta Math Hungary 113(4);2006:281–287], δ–β-continuity has given to obtain a decomposition of continuity. In this paper, we investigate the properties of δ–β-continuous functions and discuss characterizations and the relationships with related functions.

On δ–β-continuous functions

Quite recently, by using semi-open (resp.α-open, preopen,β-open) sets in a topological space, the notions ofsg*-closed (resp.αg*-closed,pg*-closedβg*-closed) sets are indroduced and investigated in [8]. These subsets place between closed sets andg-closed sets due to Levine [5]. In this paper, we introduce the notion ofmg*-closed sets and obtain the unified theory for collections of subsets between closed sets andg-closed sets.

Between closed sets and g -closed sets

The aim of this paper is to unify the concepts of topological ideals, operation functions (= expansions) and generalized closed sets.

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Unified operation approach of generalized closed sets via topological ideals

The notion of contra-continuity was introduced and investigated by Dontchev (3). In this paper, we introduce and investigate a new generalization of contra-continuity called contra-precontinuity.

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Takashi Noiri

Papers

On decompositions of continuity via idealization

On δ–β-continuous functions

Between closed sets and g -closed sets

Unified operation approach of generalized closed sets via topological ideals

On Contra-Precontinuous Functions