On Ω-closed sets and Ωs-closed sets in topological spaces

Abstract

New classes of sets called Ω-closed sets and Ωs-closed sets are introduced and studied. Also, we introduce and study Ω-continuous functions and Ωs-continuous functions and prove pasting lemma for these functions. Moreover, we introduce classes of topological spaces called Ω − T 1 2 and Ω − Ts.

On Totally Supra N-Continuous Function and Totally Supra N-Closed Map

“…(iii) supra Ω closed set (Noiri and Sayed, 2005), if sclµ(A) ⊆ intµ (U ),whenever A ⊆ U , U is supra open set. (Mashhour et al, 1983) The supra closure of a set A is denoted by clµ (A), and is defined as supra cl(A) = ∩ {B : B is supra closed and A ⊆ B}.…”

Completely Supra N-Continuous Function

“…A set A of X is called (i) supra semi-open set (Levine, 1991) (Devi et al, 2008), if A ⊆ int µ (cl µ (int µ (A))). (iii) supra Ω closed set (Noiri and Sayed, 2005), if scl µ (A) ⊆ int µ (U ), whenever A ⊆ U , U is supra open set. (iv) supra N-closed set (Vidyarani and Vigneshwaran, 2013a), if Ωcl µ (A) ⊆ U , whenever A ⊆ U, U is supra α open set.…”