Open Access Library Journal 2019, Volume 6, e5604 ISSN Online: 2333-9721 ISSN Print: 2333-9705 DOI: 10.4236/oalib.1105604 Sep. 17, 2019 1 Open Access Library Journal On Standard Concepts Using ii-Open Sets Beyda S. Abdullah, Amir A. Mohammed Department of Mathematics, College of Education for pure Sciences, University of Mosul, Mosul, Iraq Abstract Following Caldas in [1] we introduce and study topological properties of ii-derived, ii-border, ii-frontier, and ii-exterior of a set using the concept of ii-open sets. Moreover, we prove some further properties of the well-known notions of ii-closure and ii-interior. We also study a new decomposition of ii-continuous functions. Finally, we introduce and study some of the separa- tion axioms specifically 0ii T , 1ii T . Subject Areas Mathematical Analysis Keywords α-Open Set, ii-Open Set, Separation Axioms 1. Introduction The notion of α-open set was introduced by Njastad in [2]. Caldas in [1] intro- duced and studied topological properties of α-derived, α-border, α-frontier, α-exterior of a set by using the concept of α-open sets. In this paper, we intro- duce and study the same above concepts by using ii-open sets. A subset A of X is called ii-open set [3] if there exists an open set G in the topology τ of X, such that: , G X φ ≠ , ( ) A CL A G ⊆  and ( ) Int A G = , the complement of an ii-open set is an ii-closed set. We denote the family of ii-open sets in ( ) , X τ by ii τ . It is shown in [4] that each of ii τ τ ⊂ and ii τ is a topology on X. This property allows us to prove similar properties of α-open set. Also, we define ii-continuous functions and we study the relation between this type of function and continuous, semi-continuous, α-continuous and i-continuous functions. Finally, we introduce a new type of separation axioms namely 0ii T , 1ii T . We prove similar properties and characterizations of 0 T and 1 T . How to cite this paper: Abdullah, B.S. and Mohammed, A.A. (2019) On Standard Concepts Using ii-Open Sets. Open Access Library Journal, 6: e5604. https://doi.org/10.4236/oalib.1105604 Received: July 15, 2019 Accepted: September 14, 2019 Published: September 17, 2019 Copyright © 2019 by author(s) and Open Access Library Inc. This work is licensed under the Creative Commons Attribution International License (CC BY 4.0). http://creativecommons.org/licenses/by/4.0/ Open Access