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The aim of this paper is to introduce and study a new classes of functions is called pj-slightly δ-β-continuous by using ij-δ-β-open sets.
A new class of functions, called somewhat -continuous functions, has been defined and studied by making use of -open sets. Characterizations and properties of somewhat -continuous functions are presented.
Sarajevo Journal of Mathematics, 2013
A new class of functions, called slightly generalized β-continuous functions is introduced. Basic properties of slightly generalized β-continuous functions are studied. The class of slightly generalized βcontinuous functions properly includes the class of slightly β-continuous functions and generalized β-continuous functions. Also, by using slightly generalized β-continuous functions, some properties of domain/range of functions are characterized. 2010 Mathematics Subject Classification. 54C08.
2008
Abstract. In this paper, β-I-open sets are used to define and investigate a new class of functions called stongly β-I-continuous functions in ideal topological spaces. AMS subject classifications: 54C08 Key words: ideal topological spaces, β-I-open sets, strongly β-I-continuous functions
International Journal of Mathematics and Mathematical Sciences, 2001
We define a functionf:X→Yto be slightlyβ-continuous if for every clopen setVofY,f−1(V)⊂Cl(Int(Cl(f−1(V)))). We obtain several properties of such a function. Especially, we define the notion of ultra-regularizations of a topology and obtain interesting characterizations of slightlyβ-continuous functions by using it.
Generalized open sets play a very important role in general topology and they are now the research topics of many topologists worldwide. Indeed a significant theme in general topology and real analysis concerns the various modified forms of continuity, separation axioms etc., by utilizing generalized open sets. In this paper, we introduce and study a new class of function called strongly b-δ-continuous function by using the notions of b-δ-open sets and b-δ-closed sets. We investigate some of the fundamental and basic properties of this strongly b-δ-continuous function. KEYWORDSδ -open sets, b-open set, b-δ-open sets, strongly b-δ-open function.
International Journal of Advances in Mathematics, 2018
In the paper, Weak Continuity Forms, Graph Conditions and Applications, the concept of u-continuous functions are introduced and presented several applications of such functions. In the present study, by generalizing the concept of u-continuity using the notion of an α-set, introduced by O. Njastad , three classes of functions are introduced and studied.The concepts introduced here are strongly u-continuous functions, αu-continuous functions and semi-αu-continuous functions. A function g : X → Y is αu-continuous (strongly u-continuous, semi-αu-continuous) at x ∈ X, if for each α-set (α-set, open set) W which contains a closed neighborhood of g(x), there exists an α-set (open set, α-set) Vwhich contains a closed neighborhood of x and satisfies condition g(clV) ⊆ clW. If g is αu-continuous (strongly u-continuous, semi-αu-continuous) at each x ∈ X, we say g : X → Y is αu-continuous (strongly u-continuous, semi-αu-continuous) on X.
Tikrit Journal of Pure Science
In this paper, we study the concepts of contra b-I-continuity and contra b-I-openness in ideal topological spaces, and obtain several characterizations and some properties of two functions. Also, we investigate its relationship with other types of functions.
2014
New classes of functions, called somewhat �-continuous, somewhat �-open and hardly �-open functions, has been defined and studied by making use of �-open sets. Characterizations and properties of these functions are presented.
2016
Abstract. In 2008, M. Caldas and G. Navalagi [1] introduced a new class of generalized open functions called weakly δ-open functions. By introducing a new type of open functions called relatively weakly δ-open together with weakly δ-open functions, we establish a new decomposition of δ-open functions. 1.
European Journal of Pure and Applied Mathematics
In this article, we investigate some properties of strongly δθ-I-continuous functions and other types of related functions. Specially, we characterize strongly δθ-I-continuous, we investigate their relationship with other types of functions, and we study the behavior of certain topological notions under the action of these functions.
Pro Mathematica, 2014
In this paper we introduce two classes of functions called weakly δ-open and weakly δ-closed functions. We obtain their characterizations, their basic properties and their relationships with other types of functions between topological spaces.
AIMS Mathematics
In this paper, we define an almost δb-continuity, which is a weaker form of R-map and we investigate and obtain its some properties and characterizations. Finally, we show that a function f : (X, τ) → (Y, ϕ) is almost δb-continuous if and only if f : (X, τ s) → (Y, ϕ s) is b-continuous, where τ s and ϕ s are semiregularizations of τ and ϕ, respectively.
In this paper, we investigated some properties of a δα − I − open set [6] and a semi * − I − open set [6] in ideal topological spaces. Moreover, the relationships of other related classes of sets are investigated. Also, a new decomposition of continuous functions is obtained by using δ − β − I−continuous and S * − continuous functions.
We introduce and investigate the notion of strongly δ-I-continuous functions, R-I-continuous functions and strongly R-I-continuous functions in ideal topological spaces.We obtain some characterizations and properties of these functions. We also study the relationship between these functions and some other weak and strong forms of continuities in ideal topological spaces.
The main purpose of this paper is to study the notion of the δω-open sets defined by Al-Jarrah et al via δω-closure operator in [4]. We give various properties of the notions of δω-closure operator and δω-open set. Also, we introduce the notions of δ ω-continuity, ω-δ-continuity and weakly δ ω-continuity by means of δω-open sets [4]. Furthermore, we obtain several relationships, examples and counterexamples related to new classes of functions.
The notion of contra continuous functions was introduced and investigated by Dontchev. In this paper, we apply the notion of β *-closed sets in topological space to present and study a new class of functions called contra β *-continuous and almost contra β *-continuous functions as a new generalization of contra continuity.
2015
The aim of this paper is to introduce new continuous and open functions called somewhat θgs-continuous and somewhat θgs-open functions using θgs-open sets.Its various characterisations and properties are established.
viXra, 2020
In this paper, we introduce and study upper and lower slightly $\delta$-$\beta$- continuous multifunctions in topological spaces and obtain some characterizations of these new continuous multifunctions.
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2023
In this paper the notions of I-e-open set and I-e *-open set are introduced and used to define a large number of modifications of the concept of continuous function, such as (I, J)-e-continuous functions, (I, J)-e *-continuous functions, contra (I, J)e-continuous functions, contra (I, J)-e *-continuous functions, almost weakly (I, J)e-continuous functions, almost weakly (I, J)-e *-continuous functions, almost (I, J)-*.
Annals of the Alexandru Ioan Cuza University - Mathematics, 2011
β-continuity was introduced by Abd El-Monsef et al. and then it's weak forms are also studied. In this paper we continued our study on almost strongly-θ-βcontinuous functions introduced by Tahiliani and contra almost-β-continuous introduced by Baker.