Generalized Double Fuzzy Semi-Basically Disconnected Spaces

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.

This study analyzes the characteristics and functioning of Sg∗-functions, Sg∗-homeomorphisms, and Sg∗#-homeomorphisms in generalized topological spaces (GTS). A few important points to emphasize are Sg∗-continuous functions, Sg∗-irresolute functions, perfectly Sg∗-continuous, and strongly Sg∗-continuous functions in GTS and generalized primal topological spaces (GPTS). Some specific kinds of Sg∗ functions, such as Sg∗-open mappings and Sg∗-closed mappings, are discussed. We also analyze the GPTS, providing a thorough look at the way these functions work in this specific context. The goal here is to emphasize the concrete implications of Sg∗ functions and to further the theoretical understanding of them by merging different viewpoints. This work advances the area of topological research by providing new perspectives on the behavior of Sg∗ functions and their applicability in various topological settings. The outcomes reported here contribute to our theoretical understanding and establish a foundation for further research.

In this paper, we introduce the notion of an \((i,j)\)-\(\mathcal{N}\)-\(\beta\)-open set which is a generalization of an \((i,j)\)-\(\beta\)-open set in a bitopological space. Also, we investigate some of its properties and characterizations. Besides, we prove that a pairwise \((i, j)\)-\(\mathcal{N}\)-\(\beta\)-open cover that has a finite (countable) subcover is equivalent to a pairwise \(\beta\)-compact (\(\beta\)-Lindel\"{ö}f) space. Finally, we introduce an \((i, j)\)-\(\mathcal{N}\)-\(\beta\)-continuous function and an \((i, j)\)-\(\mathcal{N}\)-\(\beta\)-irresolute function and obtain some of their properties.

In spatial data modeling, the topological notion “continuous function” can link the spatial data with the modeled real world. In this article, we study fuzzy weakly continuous function and fuzzy weakly irresolute functions from set theoretic point of view. These generalizations of continuous functions in fuzzy setting will bring new practically relevant models in image processing.

In this paper, we introduce some weaker forms of vague soft continuous functions and study their characterizations. We also provide a decomposition of $V \alpha \tilde{S}$-continuous functions. Further, we introduce the notion of vague soft irresolute functions and show the concepts of vague soft continuity and vague soft irresoluteness are independent of each other.

In the present paper, we introduced a class of fuzzy G- semi open sets which is contained in class of fuzzy semi open sets. Using them fuzzy G- semi continuous functions and some special functions called fuzzy slightly G- semi continuous functions is introduced. Further it is shown in fuzzy subset theory, each fuzzy slightly G- semi continuous functions is fuzzy slightly semi continuous function.

The purpose of this study is to introduce the concept of homeomorphism via βm – closed set and study its behavior and properties in double fuzzy topological spaces. This objective is achieved through the definitions of df- βm continuous functions and df- βm closed functions. The results of this study represent important relationships and proofs, in addition to providing some necessary examples.