On supra semi open sets and some applications on topological spaces

Abstract

The purpose of this paper is to study the properties of a new class of generalized supra open sets called supra semi open. The notions of supra semi interior, supra semi closure and supra semi boundary operators are introduced and investigated. Based on the supra semi open sets, new types of supra continuous, supra open, supra closed and supra homeomorphism maps are presented and studied. In particular, the equivalent conditions for these maps are given. Some examples are included to illustrate the main results.

UTILIZING SUPRA Α-Open SETS TO GENERATE NEW TYPES OF SUPRA COMPACT AND SUPRA LINDELÖF SPACES

“…Also, we have investigated the main properties of these concepts and have illustrated the relationships among them. In a next study, we use a notion of supra R-open sets [6] to generalize some of these concepts. We hope that the results obtained in this article will help research teams promote further study in supra topological spaces to carry out a general frame work for the practical applications.…”

Supra Homeomorphism in Supra Topological Ordered Spaces

“…Apart from that, we point out the relationships among them with the help of illustrative examples. We plan to generalize the given concepts depending on a notion of R-open sets [2]. In the end, the presented concepts in this paper are a fundamental background for studying several topics in supra topological ordered spaces.…”

Some properties of an operation on g?-open sets

“…(1) If the subsets A and B are gαγ-open in (X, τ), then A ∩ B is also gαγ-open in (X, τ). (2) τ gαγ forms a topology on (X, τ).…”

“…Asaad [7] defined a γ operation on generalized open sets in X and studied its applications. In 2017-2018, Ahmad and Asaad ([1], [9]) introduced an operation γ on semi generalized open subsets of X and discussed some types of separation axioms, functions and closed spaces with respect to γ. Al-shami [4] investigated some separation axioms via supra topological spaces and he [2] introduced a concept of supra semi open sets. He [3] also studied somewhere dense sets on topological spaces and obtained interesting properties.…”

“…He [3] also studied somewhere dense sets on topological spaces and obtained interesting properties. El-Shafei et al [11] defined a type of generalized supra open sets and studied some of its applications.…”