New soft operators related to supra soft $ \delta_i $-open sets and applications

Abstract

<abstract><p>This project aimed to introduce the notion of supra soft $ \delta_i $-open sets in supra soft topological spaces. Also, we declared the differences between the new concept and other old generalizations. We presented new operators such as supra soft $ \delta_i $-interior, supra soft $ \delta_i $-closure, supra soft $ \delta_i $-boundary and supra soft $ \delta_i $-cluster. We found out many deviations to our new operators; to name a few: If $ int^s_{\delta_i}(F, E) = (F, E) $, then it doesn't imply that $ (F, E) \in SOS_{\delta_i}(X) $. Furthermore, we applied this notion to define new kinds of mappings, like supra soft $ \delta_i $-continuous mappings, supra soft $ \delta_i $-irresolute mappings, supra soft $ \delta_i $-open mappings and supra soft $ \delta_i $-closed mappings. We studied their main properties in special to distinguish between our new notions and the previous generalizations. It has been pointed out in this work that many famous previous studies have been investigated here; in fact, I believe that this is an extra justification for the work included in this manuscript.</p></abstract>

Strictly Wider Class of Soft Sets via Supra Soft δ-Closure Operator

“…Definition 2.10. [47] Let (Z, Θ, ∆) be an SSTS and (S, ∆) ∈ S(Z) ∆ . Then, supra soft δ-boundary of (S, ∆), is denoted by b s δ (S, ∆), defined by b s δ (S, ∆) = cl s δ (S, ∆) − int s δ (S, ∆).…”

“…Definition 3.3. [47] Let f pu : (Z 1 , τ 1 , ∆ 1 ) → (Z 2 , τ 2 , ∆ 2 ) be a soft function with Θ 1 as an associated SSTS with τ 1 is said to be a supra soft δ-continuous…”

“…Recently, [47], Abd El-latif defined the concept of supra soft δ-open sets in SSTSs. He introduced new soft operators named, supra soft δ-closure (interior, boundary, cluster) operator.…”