Irresolute Mappings Research Articles

New soft operators related to supra soft $ \delta_i $-open sets and applications

<abstract><p>This project aimed to introduce the notion of supra soft $ \delta_i $-open sets in supra soft topological spaces. Also, we declared the differences between the new concept and other old generalizations. We presented new operators such as supra soft $ \delta_i $-interior, supra soft $ \delta_i $-closure, supra soft $ \delta_i $-boundary and supra soft $ \delta_i $-cluster. We found out many deviations to our new operators; to name a few: If $ int^s_{\delta_i}(F, E) = (F, E) $, then it doesn't imply that $ (F, E) \in SOS_{\delta_i}(X) $. Furthermore, we applied this notion to define new kinds of mappings, like supra soft $ \delta_i $-continuous mappings, supra soft $ \delta_i $-irresolute mappings, supra soft $ \delta_i $-open mappings and supra soft $ \delta_i $-closed mappings. We studied their main properties in special to distinguish between our new notions and the previous generalizations. It has been pointed out in this work that many famous previous studies have been investigated here; in fact, I believe that this is an extra justification for the work included in this manuscript.</p></abstract>

On m∆-open sets in micro topological spaces

The aim of this article, we introduced and studied m∆-open sets in micro topological spaces. We offer a new class of sets called m∆-closed sets in micro topological spaces and we study some of its basic properties. we introduce m∆-interior and m∆- closure and study some of its basic properties. We introduce m∆-continuous maps, m∆- irresolute maps and study some of its basic properties.

Irresolute maps in topological ordered spaces

Irresolute maps in topological ordered spaces

Decomposition of Pre-β- Irresolute Maps and g- Closed Sets in Topological Space

This paper explores the decomposition of pre--irresolute (pre--irr) maps and their connection to generalized closed sets (g-closed) in topological space (top. sp.). We provide the necessary background on top. sp., continuity, closed, and related concepts. We introduce the definitions of pre--irr maps and g-closed and discuss their basic properties. The decomposition theorem is presented, stating that every pre--irr map can be decomposed into a composition of a pre--continuous (pre- -cont.) map and a b-irr map. Examples and applications are provided to illustrate the behavior of pre--irr maps and the practical implications of the decomposition theorem. We examine the relationships between pre--cont. maps and pre--irr maps, exploring the conditions under which a pre--irr map is also -irr, and provide a proof for this relationship. The properties of pre--cont. maps, - maps, g- pre--cont. maps, and g--cont. maps are discussed, along with proofs and examples to illustrate their applicability. This paper contributes to the understanding of pre--irr maps, their decomposition, and their relationships with g-closed, providing a foundation for further research in top. sp. and map decompositions. Keywords: pre-β-irresolute maps, g-closed, pre-β-cont. maps, b-cont. maps

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 .

Ifgp Continuous Mapping, Ifgp Irresolute Mapping, and Ifgp Connectedness in Intuitionistic Fuzzy Topological Spaces

Ifgp Continuous Mapping, Ifgp Irresolute Mapping, and Ifgp Connectedness in Intuitionistic Fuzzy Topological Spaces

Generalized \(\mathcal{I}_\mathcal{p}\)-Closed Sets in Ideal Topological Spaces

The main focus of this study is to introduce a new category of generalized closed sets, referred to as \(\mathcal{I}_\mathcal{p}\)- closed sets, within the framework of ideal topological spaces. By using a few instances, we demonstrate \(\mathcal{I}_\mathcal{p}\)- closed sets and establish some fundamental properties of \(\mathcal{I}_\mathcal{p}\)-closed sets. We also investigate the relationship between \(\mathcal{I}_\mathcal{p}\)-closed sets and other classes of generalized closed sets in ideal topological spaces, such as (\mathcal{I}_\mathcal{g}\)- closed sets, \(\alpha\)\(\mathcal{I}_\mathcal{g}\)-closed sets, and (\mathcal{I}_\mathcal{r}\)\mathcal{g}\)-closed sets. Then, we focus on the topological implications of \(\mathcal{I}_\mathcal{p}\)-closed sets and investigate how they relate to the concepts of \(\mathcal{I}_\mathcal{p}\)-continuous map, (\mathcal{I}_\mathcal{p}\)-irresolute map, and a strongly \(\mathcal{I}_\mathcal{p}\)-continuous map. First and foremost, we define the \(\mathcal{I}_\mathcal{p}\)-continuous map, investigate the behavior of \(\mathcal{I}_\mathcal{p}\)- continuous map with respect to \(\mathcal{I}_\mathcal{p}\)-closed sets, and derive several important properties of \(\mathcal{I}_\mathcal{p}\)-continuous map. Further, we studied their relationships with other classes of continuous maps in ideal topological spaces. Nevertheless, we defined the definitions of \(\mathcal{I}_\mathcal{p}\)-irresolute maps and strongly \(\mathcal{I}_\mathcal{p}\)-continuous maps in ideal topological spaces. We explored the connections with the notions of \(\mathcal{I}_\mathcal{p}\)-continuous map, (\mathcal{I}_\mathcal{p}\)-irresolute map, and a strongly \(\mathcal{I}_\mathcal{p}\)-continuous map. Our results provide new insights into the study of ideal topological spaces.

Contra M -Continuous Maps in Neutrosophic Soft Topological Spaces

In this paper, we introduce, study, and explain some of the properties of neutrosophic soft contraM-continuous mappings and irresolute maps in neutrosophic soft topological spaces.

Ic-Separation Axioms in Topological Spaces

A new class of separation axioms known as ic-separation axioms is introduced in this study. They rely on new extended open sets known as ic-open sets, and we describe the relationship between them and give several examples. Additionally, we define ic-generalized closed set concepts in a topological space in order to frame the another class of separation axioms called ic-generalized axioms. Among other things, the basic concern properties and relative preservation properties of these spaces are projected under ic-generalized irresolute mappings.

Fuzzy totally semi alpha-irresolute mappings

The aim of this article is to introduce two new classes of mappings called fuzzy totally semi -irresolute mapping and fuzzy totally almost irresolute mapping. Moreover, their characterizations , examples and compositions of these mappings, their relationships between other fuzzy mappings are studied.

Nncβ-CONTINUOUS MAPS

In this article, we study a new types of mappings using N-neutrosophic crisp β open sets such as continuous mappings and irresolute mappings in Nneutrosophic crisp topological spaces were introduced. Also, we discussed about their properties in relation with the other continuous and irresolute mappings in N-neutrosophic crisp topological spaces. Also, we study about the concept of strongly N-neutrosophic crisp β continuous and perfectly N-neutroso

Hα-Open Sets in Topological Spaces

In our work we introduced a new type of open sets is defined as follows: If for each set that is not empty M in X, M≠X and M ∈τ^∝such that A ⊆ int(A∪M). then A in (X,τ) is named h∝-open set. We also go through the relationship between h∝- open sets and a variety of other open set types as h-open sets, open sets, semi-open sets and ∝-open sets. We proved that each h-open and open set is h∝-open and there is no relationship between∝-open sets and semi-open sets with h∝-open sets. Furthermore, we begin by introducing the concepts of h∝-continuous mappings, h∝-open mappings, h∝-irresolute mappings, and h∝-totally continuous mappings, We proved that each h-continuous mapping in any topological space is h∝-continuous mapping, each continuous mapping in any topological space is h∝-continuous mapping and there is no relationship between∝-continuous mappings and semi-continuous mappings with h∝-continuous mappings as well as some of its features. Finally, we look at some of the new class's separation axioms.

Some (Lambda,b)-type mappings in topological spaces

We introduce and study (Lambda, b)-continuous, (Lambda, b)-irresolute and quasi-(Lambda, b)-irresolute mappings. Some characterizations and several properties concerning aforesaid mappings are obtained. The authors also introduce (Lambda, b)-compactness and (\Lambda, b)-connectedness. It is proved that (Lambda, b)-compactness (respectively (\Lambda, b)-connectedness) is preserved under (\Lambda, b)-irresolute mappings. The paper also touches the topics frontier points, Dirichlet's function, filter and algebraic structure of some functions.

Nncγ Maps in Nnc-Topological Spaces

In this article, the concept of N-neutrosophic crisp γ-open and N-neutrosophic crisp γ-closed mappings in N-neutrosophic crisp topological spaces are introduced and studied some of their related properties. Also, Nneutrosophic crisp γ irresolute mapping is introduced in N-neutrosophic crisp topological spaces. Further, it is extended to N-neutrosophic crisp γ-homeomorphism, N-neutrosophic crisp γ-Completely homeomorphism and N-neutrosophic crisp γT1/2-space in N-neutrosophic crisp topological spaces and establishes some of their related properties. Finally, Strongly N-neutrosophic crisp γ continuous and Perfectly N-neutrosophic crisp γ continuous functions is also discuss.

Intuitionistic fuzzy semi δ-pre irresolute mappings

This paper introduces the concept of intuitionistic fuzzy semi δ-pre irresolute mappings in intuitionistic fuzzy topological spaces. We investigate some of their properties and obtain several preservation properties and characterizations.

On infra generalized #α-closed sets in infra topological spaces

In this paper, the relatively new notions of Infra generalized #α- closed set, Infra generalized #α- continuous functions, Infra generalized #α- irresolute mappings are introduced and explored some of its characteristics.

£-Single Valued Extremally Disconnected Ideal Neutrosophic Topological Spaces

This paper aims to mark out new concepts of r-single valued neutrosophic sets, called r-single valued neutrosophic £-closed and £-open sets. The definition of £-single valued neutrosophic irresolute mapping is provided and its characteristic properties are discussed. Moreover, the concepts of £-single valued neutrosophic extremally disconnected and £-single valued neutrosophic normal spaces are established. As a result, a useful implication diagram between the r-single valued neutrosophic ideal open sets is obtained. Finally, some kinds of separation axioms, namely r-single valued neutrosophic ideal-Ri (r-SVNIRi, for short), where i={0,1,2,3}, and r-single valued neutrosophic ideal-Tj (r-SVNITj, for short), where j={1,2,212,3,4}, are introduced. Some of their characterizations, fundamental properties, and the relations between these notions have been studied.

On Πg(αg)* – continuous maps and Πg(αg)* - irresolute maps in Topological Spaces

On Πg(αg)* – continuous maps and Πg(αg)* - irresolute maps in Topological Spaces

Generalized closed fuzzy soft sets in Čech fuzzy soft closure spaces

In this paper, we present the concept of generalized closed fuzzy soft sets in the Čech fuzzy soft closure spaces, termed g-closed fss’s, and investigate their basic properties. By using g-closed fss’s, we define a new fuzzy soft closure operator which is generates a new fuzzy soft topology finer than that induced from the Čech fuzzy soft closure operator. In addition, we define generalized Čech fuzzy soft continuous (respectively, irresolute) mapping by means of g-closed fss’s. As application of these sets, -Čech fuzzy soft closure spaces are introduced and discuses.

A NOTE ON INTUITIONISTIC FUZZY GENERALIZED IRRESOLUTE MAPPINGS

In this paper a new class of mapping called intuitionistic fuzzy -generalized semi irresolute mapping in intuitionistic fuzzy topological space is introduced and some of its properties are studied.