In this paper, a new kind of sets called Dα-open sets are introduced and studied in a topological space. The class of all Dα-open sets is strictly between the class of all α-open sets and g-open sets. Also, as applications we introduce and study Dα-continuous, Dα-open, and Dα-closed functions between topological spaces. Finally, some properties of Dα-closed and strongly Dα-closed graphs are investigated.
© 2015 Mansoura University. Production and hosting by Elsevier B.V.

In this paper, the concepts of Ω^*-closed and Ω*-continuous maps are introduced and several properties of them are investigated. These concepts are used to obtain several results concerning the preservation of Ω-closed sets. Moreover, we use Ω^*-closed and Ω^*-continuous maps to obtain a characterization of semi-T_1/2-spaces.

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The aim of this paper is to introduce and study the concepts of Ωs^*-closed and Ωs^*-continuous maps. These concepts are used to obtain several results concerning the preservation of Ωs-closed sets. Moreover, we use Ωs^*-closed and Ωs^*-continuous maps to obtain a characterization of Ω - T_1/2-spaces.

 

For dealing with uncertainties researchers introduced the concept of soft sets. Georgiou et al. [10] defined several basic notions on soft θ-topology and they studied many properties of them. This paper continues the study of the theory of soft θ-topological spaces and presents for this theory new definitions, characterizations, and results concerning soft θ-boundary, soft θ-exterior, soft θ-generalized closed sets, soft Λ-sets, and soft strongly pu-θ-continuity.

In the present paper, we introduce topological notions defined by means
of α-open sets when these are planted into the framework of Ying’s
fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T 0 α -; T 1 α -; T 2 α  (α- Hausdorff)-, T 3 α  (α-regular)- and T 4 α  (α-normal)-separation axioms. Furthermore, the R 1 α - and R 2 α -separation axioms are studied and their relations with the T 1 α - and T 2 α -separation axioms are introduced. Moreover, we clarify the relations of these axioms with each other as well as the relations with other
fuzzifying separation axioms.

In this paper, some characterizations of fuzzifying g -compactness are given,
including characterizations in terms of nets and g -subbases. Several characterizations of locally g -compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

© 2015 International Fuzzy Mathematics Institute-Los Angeles

In this paper, some characterizations of fuzzifying semi-compactness are given, including characterizations in terms of nets and semi-subbases. Lastly, several characterizations of locally semi-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

© 2014 – IOS Press and the authors.
 

This paper is a continuation of [1]. That is, it considers fuzzifying topologies, a special case of I-fuzzy topologies (bifuzzy topologies), introduced by Ying [2]. It investigates topological notions defined by means of a-open sets when these are planted into the framework of Ying’s fuzzifying topological spaces (by Łukasiewicz logic in [0,1]). Other characterizations of fuzzifying compactness are given, including characterizations in terms of nets and a-subbases. Several characterizations of locally a-compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

@2013 Production and hosting by Elsevier B.V. on behalf of Egyptian Mathematical Society.
 

In the present paper, we introduced topological notions defined by means of regular open sets when these are planted into the framework of Ying’s
fuzzifying topological spaces (in Lukasiewicz fuzzy logic). We used fuzzy logic to introduce almost separation axioms T0R-; T1R-; T2R(almost Hausdorff)-, T3R (almost regular)- and T4R (almost-normal). Furthermore, the R0Rand  R1R-separation axioms have been studied and their relations with the T1R- and T2R-separation axioms have been introduced. Moreover, we gave the relations of these axioms with each other as well as the relations with other fuzzifying separation axioms.

@ 2013 Modern Science Publishers.
 

In this paper, the concept of supra b-irresolute maps is introduced and several
properties of it is investigated. Furthermore, the notion of supra b-connectedness is defined and researched by means of supra b-separated sets.

http://dx.doi.org/10.5666/KMJ.2013.53.3.341