Functions In Topological Spaces Research Articles

Almost SpgΑ -Continuous Functions in Topological Spaces

Almost SpgΑ -Continuous Functions in Topological Spaces

G**β-Continuous and G**β-Irresolute Mappings in Topological Spaces

Topology being somehow very recent in nature but has got tremendous applications over almost all other fields. Theoretical or fundamental topology is a bit dry but the application part is what drives crazy once we get used. Topology has applications in various fields of Science and Technology, like applications to Biology, Robotics, GIS, Engineering, Computer Sciences. Topology though being a part of mathematics but it has influenced the whole world with so strong effects and incredible applications. The concept of continuity is fundamental in large parts of contemporary mathematics. In the nineteenth century, precise definitions of continuity were formulated for functions of a real or complex variable, enabling mathematicians to produce rigorous proofs of fundamental theorems of real and complex analysis, such as the Intermediate Value Theorem, Taylor’s Theorem, the Fundamental Theorem of Calculus, and Cauchy’s Theorem. In the early years of the Twentieth Century, the concept of continuity was generalized so as to be applicable to functions between metric spaces, and subsequently to functions between topological spaces. Topology is an area of mathematics concerned with the properties of space that are preserved under continuous deformations including stretching and bending but not tearing. In 2023, Dr. T. Delcia and M. S, Thillai introduced a new type of closed sets called g**β-closed sets and investigated their basic properties including their relationship with already existing concepts in Topological Spaces. In this paper, we introduce g**β-continuous function, g**β-irresolute function, g**β-open function, g**β-closed function, pre-g**β-open function, and pre-g**β-closed function, and investigate properties and characterizations of these new types of mappings in topological spaces.

New Forms of alphag - continuous Maps in Topology

Abstract: In this paper, we describe a novel class of continuous maps called as strongly alpha generalised continuous maps in topological spaces. Furthermore, we investigate their properties with existing continuous maps, and we also study their decomposition of continuous functions.

Parametric topological entropy of families of multivalued maps in topological spaces and induced hyperspace maps

A positive parametric topological entropy is examined whether or not it is preserved from given continuous maps to the induced hyperspace maps. An established affirmative answer generalizes all the related results obtained in this field so far, because the continuous maps under consideration can be multivalued and nonautonomous (time-dependent) in compact topological Hausdorff spaces. A variety of definitions of parametric topological entropy for multivalued maps is investigated, together with their properties. Several simple illustrative examples are supplied.

On some contractive mappings and a new version of implicit function theorem in topological spaces

Study on existence of fixed points of contraction and contractive (type) mappings in topological spaces is a challenging task. The main goal of this article is to deal with this challenging task. To achieve our goal, we define two new contractive type mappings, namely, h-A-contractive and h-A1-contractive mappings on a topological space X, where h : X ? X ? R+ is a function and A, A1 are two collections of implicit functions. Then, we obtain some fixed point results concerning such contractive type mappings. Finally, as an application of one of the above mentioned fixed point results, we obtain a newer version of the implicit function theorem in topological spaces.

New results for certain types of contra pre-continuous functions in topological space

The aim of this work, introduce some properties of another type of contra pre-continuous functions in topological space up on some generalization of closed sets, namely pre-closed and preopen sets as well as showing some theorems related about to composition and restriction for these types of functions, also submitted another types ofcontra-continuous which are bi-contra-continuous functions with several theorems about this concept have been given.

On Еc-Continuous and δ-ßc-Continuous Mappings in Topological Spaces Via Еc-open and δ-ßc-open sets

In the present paper, new concepts of generalized continuous mappings, namely Еc and δ-ßc-continuous mappings have been introduced and studied by using a new generalized of open sets Еc and δ-ßc-open sets ,respectively. Several characterizations and fundamental properties of these forms of generalized continuous mappings are obtained. Moreover, the graphs of Еc-continuous and δ-ßc-continuous mappings have been investigated. In addition, the relationships among Еc-continuous and δ-ßc-continuous mappings and other well-known forms of generalized continuous mappings in topological spaces are also discussed.

Topological entropy of multivalued maps in topological spaces and hyperspaces

The main aim of this article is two-fold: (i) to correct some discrepancies in our recent paper entitled “Chaos for multivalued maps and induced hyperspace maps”[Chaos, Solitons & Fractals 138(2):109898, 1–8, 2020], (ii) to generalize the investigation analysis to multivalued maps in compact Hausdorff topological spaces. We will introduce various (some newly) definitions of topological entropy for multivalued maps and test whether or not their positive entropy implies the same for induced hyperspace maps. All of them reduce to the standard definition for single-valued maps. On the other hand, they exhibit different properties. In particular, only some definitions share the above implication (forcing property) with single-valued maps. Several illustrative examples are supplied.

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.

New Form Of Continuous Functions In Topological Spaces

New Form Of Continuous Functions In Topological Spaces

Some new results of difference perfect functions in topological spaces

<abstract><p>Everyday problems are characterized by voluminous data and varying levels of ambiguity. Thereupon, it is critical to develop new mathematical approaches to dealing with them. In this context, the perfect functions are anticipated to be the best instrument for this purpose. Therefore, we investigate in this paper how to generate perfect functions using a variety of set operators. Symmetry is related to the interactions among specific types of perfect functions and their classical topologies. We can explore the properties and behaviors of classical topological concepts through the study of sets, thanks to symmetry. In this paper, we introduce a novel class of perfect functions in topological spaces that we term D-perfect functions and analyze them. Additionally, we establish the links between this new class of perfect functions and classes of generalized functions. Furthermore, while introducing the herein proposed D-perfect functions and analyzing them, we illustrate this new idea, explicate the associated relationships, determine the conditions necessary for their successful application, and give examples and counter-examples. Alternative proofs for the Hausdorff topological spaces and the D-compact topological spaces are also provided. For each of these functions, we examine the images and inverse images of specific topological features. Lastly, product theorems relating to these concepts have been discovered.</p></abstract>

On $B^{ic}$-open set and $B^{ic}$-continuous function in topological spaces

In this paper, we have introduced a new class of sets in topological space called $B^{ic}$-open set and we have introduced and study the properties of $B^{ic}$-continuous function and topological properties.

Properties and Applications of d*g? - Closed Sets in Topological Spaces

We introduce the concept of d*g?-closed sets in a topological space and investigate their properties. Moreover, we investigate new separation axioms and new functions in topological spaces.

On perfectly αδ-continuous functions in topological spaces

The concept of αδ-closed sets was introduced in the research paper “On Strongly-αδ-Super-Irresolute Functions In Topological Spaces. The aim of this paper is to consider and characterize αδ-irresolute and αδ-continuous functions via the concept of αδ-closed sets and to relate these concepts to the classes of αδ-compact spaces and αδ0-connected spaces.

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.

On $alpha^{*}-$continuous and contra $alpha^{*}-$continuous mappings in topological spaces with soft setting

In this work, some new connotations of continuous mappings such as $alpha^{*}$ - continuous mapping $left(alpha^{*}-C Mright),$ irresolute $alpha^{*}-$mapping $left(I alpha^{*}-C Mright),$ and strongly $alpha^{*}-$ continuous mapping $left(S alpha^{*}-C Mright)$ are studied and some of their characteristics are discussed. In other side, new some classes of contra continuous mappings are investigated in this work, they are called contra $alpha^{*}$ - continuous mapping $left(C alpha^{*}-C Mright)$.

On Approximately w-Continuous Function in Topological Spaces

On Approximately w-Continuous Function in Topological Spaces

On D-closed maps and D-open maps in topological spaces

In this paper, we introduce D-closed map from a topological space X to a topological space Y as the image of every closed set is D-closed and also we prove that the composition of two D-closed maps need not be Db-closed map. We also obtain some properties of D-closed maps.

Characterizations of Completely Nnc (Weakly Nnc )-irresolute Functions via Nnce-open Sets

The purpose of present this paper is to introduce and investigate two new classes of Nnc -irresolute functions called completely Nnce-irresolute functions and completely weakly Nnce-irresolute functions in topological spaces by using the concept of Nnce-open sets. Several new characterizations and interesting properties concerning completely Nnce-irresolute functions and completely weakly Nnce-irresolute functions are obtained. Furthermore the relationships between these functions and some other well-known types of functions are also given.

An Analysis of ψ*rs – Closed Sets and ψ*rs – Continuous Functions in Topological Spaces

In this paper, we introduce the concept of ψ*rs – closed sets and investigate their properties. We analyses the relations between ψ*rs – closed sets with already existing closed sets. Also, we introduce ψ*rs – continuity in this paper.