A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

The aim of this paper is to introduce various functions associated with semi*α-open sets. Here semi*αcontinuous, semi*α-irresolute, contra-semi*α-continuous and contra-semi*α-irresolute functions are defined. Characterizations for these functions are given. Further their fundamental properties are investigated. Many other functions associated with semi*α-open sets and their contra versions are ...

In this paper, we extend the notions of γ-operation introduced in [12], by using the soft ideal notions. We introduce the notions of Ĩ-open soft sets, pre-Ĩopen soft sets, α-Ĩ-open soft sets, semi-Ĩ-open soft sets and β-Ĩ-open soft sets to soft topological spaces. We study the relations between these different types of subsets of soft topological spaces with soft ideal. We also introduce the co...

The notions of pre-local function, semi-local functions and α-local functions with respect to a topology and an ideal are introduced, and several properties are investigated. Also, the concept of P -I-open sets and P -I-closed sets in ideal topological spaces are discussed. Relations between I-open sets and P -I-open sets are provided, and several properties related to P -I-open sets, pre-local...

In this paper a new generalization of semi-open maps via the concept of sg-closed sets is considered. They are called approximately semi-open maps and are used to obtain a characterization of semi-T1/2 spaces.

Azad [1] introduced the concepts of fuzzy semi-open sets and fuzzy semi-continuous mappings. Fuzzy α-open sets and fuzzy α-continuous functions were introduced by Mashhour et. al. [4] and Singal et. al. [6] respectively. The concepts of fuzzy pre-open sets and fuzzy pre-continuous mappings were introduced by Bin Sahana [2]. In this paper the concepts of fuzzy α-quotient maps, fuzzy semi quotien...

Several specific types of generalized sets (briefly, g-T_g-sets in topological spaces T_g-spaces have been defined and investigated for various purposes from time to the literature T_g-spaces. Our recent research field a new class is reported herein as starting point more classes. It shown that superclass those whose elements are called open, closed, semi-open, semi-closed, pre-open, pre-closed...

in this paper, a new class of multifunctions, called generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions, has been dened and studied. some characterizations and severalproperties concerning generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions are obtained. the re-lationships between generalized alpha (mu_{x};mu_{ y} )-continuous multifunctions and some known con-ce...