New versions of maps and connected spaces via supra soft sd-operators

Abstract

In this manuscript we use novel types of soft operators to define new approaches of soft maps in the frame of supra soft topologies (or SSTSs), namely supra soft somewhere dens continuous (or SS-sd-continuous), SS-sd-open and SS-sd-closed maps. With the help of SS-closure (interior) operators and SS-sd-closure (interior) operators we succeed to introduce many equivalent conditions and several important properties to these notions. To name a few: We prove that there is an one to one between the SS-sd-open and SS-sd-closed maps under a bijective soft map, supported by counterexample to confirm the necessity of the bijectivity condition. Furthermore, we present the concept of SS-sd-separated sets with intersected characterizations, as a prelude to studying the connectedness in a supra soft topological space (or SSTS). Moreover, we show that, there is no priori relationship between supra soft-sd-connectedness in an SSTS and its parametric supra topological spaces in general, supported by concrete counterexamples. Finally, we prove that the image of an SS-sd-connected set under an SS-sd-irresolute map is an SS-sd-connected.