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 separation axioms specifically T0ii, T1ii.
Cite this paper
Abdullah, B. S. and Mohammed, A. A. (2019). On Standard Concepts Using ii-Open Sets. Open Access Library Journal, 6, e5604. doi: http://dx.doi.org/10.4236/oalib.1105604.
Caldas, M. (2003) A Note on Some Applications of α-Open Sets. International Journal of Mathematics and Mathematical Sciences, 2, 125-130. https://doi.org/10.1155/S0161171203203161
Levine, N. (1963) Semi-Open Sets and Semi-Continuity in Topological Spaces. The American Mathematical Monthly, 70, 36-41. https://doi.org/10.2307/2312781
