Abstract
The purpose of this paper is to investigate the concepts of minimal and maximal regular open sets and their relations with minimal and maximal open sets. We study several properties of such concepts in a semi-regular space. It is mainly shown that if X is a semi-regular space, then miO(X) = miRO(X). We introduce and study new type of sets called minimal regular generalized closed. A special interest type of topological space called rTmin space is studied and obtain some of its basic properties.
Highlights
Introduction and PreliminariesA subset A of a topological space (X, τ ) is called a semi-open [14] set if A ⊆ Cl(Int(A))
The family of all semi-open sets is denoted by SO(X)
The family of all regular-open sets is denoted by RO(X, τ ) or RO(X)
Summary
A subset A of a topological space (X, τ ) is called a semi-open [14] (resp. a preopen [1], an α-open [16]) set if A ⊆ Cl(Int(A)) A subset A of a topological space X is said to be a regular open set [10] if A = Int(Cl(A)) It is called a regular closed if Ac is a regular open. [11] Let X be a topological space and U a any nonempty subset S of U is preopen set. A nonempty proper regular open set A of a topological space (X, τ ) is said to be:. Minimal regular closed, maximal regular open, maximal regular closed) sets in a topological space (X, τ ) is denoted by miRO(X, τ ) Let V be a nonempty finite regular open set in a topological space X. If V is a nonempty open set, there exists at least one (finite) minimal regular open set U such that U ⊆ V. By Theorem 1.16, there exists a minimal regular open set U such that U ⊆ A
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
