Other new types of Mappings with Strongly Closed Graphs in Topological spaces via e-θ and δ-β-θ-open sets

Abstract

The purpose of this paper is to introduce and investigate a new types of mappings with Strongly Closed Graphs in Topological spaces namely strongly e-θ-(resp. δ-βθ)-Closed Graphs by using the concepts of e-θ-(resp. δ-βθ)-open sets and e-θ-(resp. δ-βθ)-closure operator which were introduced by Murad ÄOzkoc and GÄulhan Aslim [1] (resp. Alaa. M. F, and Xiao-Song Yang [2]), several characterizations and fundamental properties concerning of such these mappings have been studied. Furthermore, some characterizations of strongly e-θ-(δ-βθ)-Closed Graphs and nearly Φ-compact spaces have been obtained.

Decision-making techniques based on similarity measures of possibility interval fuzzy soft environment

“…Then, these measures are applied to the medical diagnosis to discover if the patient has dengue fever or not. Finally, for further work on these topics, we recommend developing these tools by integrating them with some other mathematical structures, such as algebraic structures [36]- [37], topological structures [38]- [39], and other ideas [40]- [43]. these properties emerge from the laws and properties of set theory to which the fuzzy theory belongs and its extension.…”

On Some Functions Related to e*-θ-open Sets

“…We shall use the well-known accepted language almost in the whole of the proofs of the theorems in this article. Lemma 2.1 [10,11] Let X be a topological space and A, B ⊆ X . Then the following properties are hold:…”

On Weakly e*-θ-open Functions and Their Characterizations

“…We shall use the well-known accepted language almost in the whole of the proofs of the theorems in this article. The following basic properties of e * -θ-closure is useful in the sequel: Lemma 1.1 ( [13,14]). Let A be a subset of a space X, then the following properties hold:…”