Irresolute Functions Research Articles

On $\psi$ gs-Functions in Bitopological Spaces

A subset $A$ of a bitopological space $(X,\tau_1,\tau_2)$ is called \emph{$(i,j)$-$\psi$gs-closed} set if\\ $(i,j)\text{-}\psi cl(A)\subseteq U$ whenever $A\subseteq U$, $U$ is $(i,j)$-semi-open in $(X,\tau_1,\tau_2)$. In this work, the propertiesof this set are considered to investigate the concepts of $\psi gs$-functions in bitopological spaces. Specifically, this study establishes some properties and provide characterizations of $\psi gs$-open and $\psi gs$-closed functions, $\psi gs$-continuous functions, and $\psi gs$-irresolute functions in bitopological spaces.

Properties of $s\tilde{\theta}$-open Sets in Generalized Topological Spaces

A study of $\tilde{\theta}$-open sets in generalized topological spaces started in 2011 by Min \cite{wkm}. In this paper, we introduce the concepts of $s\tilde{\theta}$-open sets, $s\tilde{\theta}$-closed sets, $s\tilde{\theta}$-continuous functions and $s\tilde{\theta}$-irresolute functions on generalized topological spaces. We also study some basic propertiesof such sets and functions.

Neutrosophic Semi <i>β<sup>F</sup></i>-Contra Continuity in a Neutrosophic Topological Space

The main intention of this article is to propose the theory of a neutrosophic SβF contra continuous function, neutrosophic strongly SβF continuous function, neutrosophic strongly SβF contra continuous function and neutrosophic SβF contra irresolute function in neutrosophic topological spaces. Further several properties based on the above concepts have been studied. Many theorems based on the above ideas have been proved with the suitable illustration. Further the relationship connecting neutrosophic SβF contra continuous function, neutrosophic strongly SβF continuous function, neutrosophic strongly SβF contra continuous function and neutrosophic SβF contra irresolute function are studied and illustrated. Moreover, various theorems based on compositions of functions have been proved. In addition to this, theproduct of two neutrosophic sets is defined and related theorems have been proved.

Soft Semi Star Star Generalized Continuous Functions

Recently soft generalized closed sets play important role in studying separation axioms in soft topological spaces. The aim of the present communication is to introduce the concepts of soft semi star star generalized continuous functions and soft semi star star generalized irresolute functions and study their basic properties in soft topological spaces.

Three Classes of Soft Functions Via Soft -Open Sets and Soft -Closed Sets

This paper introduces novel concepts of soft functions known as soft -irresolute, soft -open, and soft -closed function as well as some of their properties. The interrelationships of this newly defined soft functions with other types of soft functions are investigated, and the behaviors of soft -irresolute (resp., soft -open, and soft -closed) functions under soft composition are studied. Finally, using soft -open sets, the concepts of soft -Hausdorff space are introduced and investigated.

On θg**- Closed Sets in Topological Spaces

In this paper we have introduced a new class of closed in topological spaces called g**-closed sets and study some of its properties . Further we introduce the concept g**-continuous functions , g**-irresolute functions . As an application we introduce two news paces namely . T **-space, **T - space .Further, g**-continuous, and g**-irresolute mappings are also introduced and investigated .

ӼϢ-connected Spaces

In this paper, we introduced a new type of open set in generalized topological spaces: ӼϢ-open set. A new generalization of connectedness in a generalized topological space using ӼϢ-open namely ӼϢ-connectedness is defined. Also, new generalizations of continuous functions in generalized topological space will be studied here as weakly ӼϢ- continuous, strongly ӼϢ- continuous and ӼϢ- irresolute functions.

Soft functions via soft semi ω -open sets

In this paper, we introduce the concepts of soft semi \( \omega \)-continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \) -irresolute functions by using soft semi \(\omega \)-open sets. We characterize them and discuss their main properties with the help of examples. We investigate under what conditions the restriction of soft semi \( \omega \)-continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \) -irresolute functions are respectively soft semi \(\omega \)-continuous, soft \( \omega \)-irresolute, and soft semi \(\omega \)-irresolute. Also, we investigate under what conditions the composition of two soft semi \(\omega \) -continuous, soft \(\omega \)-irresolute, and soft semi \(\omega \)-irresolute functions are respectively soft semi \(\omega \)-continuous, soft \(\omega \) -irresolute, and soft semi \(\omega \)-irresolute. In addition to these, we examine the connection between the new classes of soft functions and their corresponding general topological concepts.

Soft bi-continuity and related soft functions

In this article, we start with some properties of several types of soft continuous and soft open functions. We primarily focus on studying soft continuous (soft open) and soft irresolute (soft anti-irresolute) functions. We show that soft continuous and soft irresolute functions are independent and correspondingly soft open and soft anti-irresolute functions. On the other hand, soft bi-continuity implies soft bi-irresoluteness but not the other way round. Moreover, we find conditions under which soft bi-irresoluteness and soft bi-continuity are similar.

On Continuity of Grill Topological Spaces VIA Regular Generalized G\(\omega\) - Closed Sets

Aims/ Objectives: In this paper, we study the continuity property in grill topological spaces via generalized G\(\omega\) -closed sets and regular generalized G\(\omega\) - closed sets. These notions are generalized G\(\omega\) - continuous functions which is weak form of g\(\omega\) - continuous functions, generalized G\(\omega\) - irresolute functions, regular generalized G\(\omega\) - continuous functions which is weak form of rg\(\omega\)continuous functions, regular generalized G\(\omega\) - irresolute functions and investigates some of its properties in grill topological spaces.

Generalized ωe∗-closed Sets

The aim of this paper is to introduce and study a new type of generalized closed sets, called generalized ωe∗ -closed (briefly, gωe∗ -closed) sets, via ωe∗-closure operator. We examine the fundamental properties of the class of these sets. The notion of gωe∗-closed set is weaker than the notions of gωβ-closed set and ωe∗-closed set in the literature. Also, we define and discuss the notions of generalized ωe∗-continuous and generalized ωe∗-irresolute functions.

On irresolute functions in ideal topological spaces

In the ideal topological spaces (X, ?, I) and (Y, J, ?), we define (I, J)-irresolute function, weakly-(I, J)-irresolute, strongly-(I, J)-irresolute functions, semi-I-open sets and quasi-H-closed spaces modulo ideal I. We discuss properties of (I, J)-irresolute function mapping connected, closed, compact ideal spaces modulo I and semi-I-isolated points. (I, J)-Homeomorphisim on presemi-I-open sets and closure properties of quasi-H-closed spaces and semi-I-open subsets are explored in this paper.

On generalized γµ-closed sets and related continuity

Abstract In this paper our main interest is to introduce a new type of generalized open sets defined in terms of an operation on a generalized topological space. We have studied some properties of this newly defined sets. As an application, we have introduced some weak separation axioms and discussed some of their properties. Finally, we have studied some preservation theorems in terms of some irresolute functions.

A unified theory for irresolute functions

In this paper, a new class called (µ, λ)θ -irresolute functions has been defined with the notion of generalized topology. We obtain some characterizations of such functions and some relations between similar types of functions are established. Some basic properties of such functions are also discussed. Such functions unify different types of weakly irresolute functions by T. Noiri.

Via semi α-regular weakly in ideal topological spaces on continuous and irresolute functions

A new class of closed sets, known as semi-regular weekly closed sets, is introduced in ideal topological space. In addition, we define a new class of continuous functions known as semi-regular weekly -continuous functions is introduced and studied. Some of their characteristics have also been examined and discussed interesting properties of semi-regular weekly -irresolute functions, strongly semi-regular weekly -continuous functions, and semi- regular weekly -continuous functions.

\U0001d478 ℐ Tαm continuous functions and Q F highly disconnectedness space

The purpose of this paper is to discuss about \U0001d478 ℐ T α m continuous functions and initiate new class of function called \U0001d478 ℐ T α m irresolute function. Also a new class of \U0001d478 ℐ topological space called \U0001d478 ℐ T α m Highly Disconnectedness Space is introduced. On this basis, some interesting properties of these spaces have been obtained.

A New Representation of Semiopenness of L-fuzzy Sets in RL-fuzzy Bitopological Spaces

In this paper, we introduce a new representation of semiopenness of L-fuzzy sets in RL-fuzzy bitopological spaces based on the concept of pseudo-complement. The concepts of pairwise RL-fuzzy semicontinuous and pairwise RL-fuzzy irresolute functions are extended and discussed based on the (i,j)-RL-semiopen gradation. Further, pairwise RL-fuzzy semi-compactness of an L-fuzzy set in RL-fuzzy bitopological spaces are given and characterized. As RL-fuzzy bitopology is a generalization of L-bitopology, RL-bitopology, L-fuzzy bitopology, and RL-fuzzy topology, the results of our paper are more general.

Beta- Star- Continuity and Beta- Star- Contra- Continuity

In 2014 Mubarki, Al-Rshudi, and Al- Juhani introduced and studied the notion of a set in general topology called β*-open set and investigated its fundamental properties and studied the relationships between β*-open set and other topological sets including β*-continuity in topological spaces. We introduce and investigate several properties and characterizations of a new class of functions between topological spaces called β*- open, β*- closed, β*- continuous and β*- irresolute functions in topological spaces. We also introduce slightly β*- continuous, totally β*- continuous and almost β*- continuous functions between topological spaces and establish several characterizations of these new forms of functions. Furthermore, we also introduce and investigate certain ramifications of contra continuous and allied functions, namely, contra β*- continuous, and almost contra β*-continuous functions along with their several properties, characterizations and natural relationships. Moreover, we introduce new types of closed graphs by using β*- open sets and investigate its properties and characterizations in topological spaces.

αg_Ị-open sets and αg_Ị-functions

The objective of this paper is to show modern class of open sets which is an -open. Some functions via this concept were studied and the relationships such as continuous function strongly -continuous function -irresolute function -continuous function.

Neutrosophic Pre-𝜶, Semi- 𝛂 & Pre- 𝜷 Irresolute Functions

Neutrosophic Pre-𝜶, Semi- 𝛂 & Pre- 𝜷 Irresolute Functions