Further notions related to new operators and compactness via supra soft topological spaces -by M. E. El-Shafei, M. Abo-Elhamayel and T. M. Al-shami

Further notions related to new operators and compactness via supra soft topological spaces-by M. E. El-Shafei, M. Abo-Elhamayel and T. M. Al-shami

Abstract: The first objective of this paper, is to study the properties of supra soft limit points with the help of a soft point notion and to introduce the notions of supra soft boundary and supra soft closure operators. With regard to these notions, we describe a supra soft closure operator in terms of supra soft limit points; and generate a unique supra soft topology by using a specific soft mapping. Also, we define relative supra soft topologies and deduce some results which connect supra soft closure and supra soft interior operators via the original supra soft topologies and their relative supra soft topologies. The second objective, is to present the concepts of supra soft compact (supra soft Lindel\"{o}f), almost supra soft compact (almost supra soft Lindel\"{o}f) and mildly supra soft compact (mildly supra soft Lindel\"{o}f) spaces in supra soft topological spaces; and to investigate their main features. Throughout this investigation, we point out the relationships among these concepts and characterize each one of them. Also, we explore the notions of soft $S^\star$-continuous mappings and prove that the image of the kinds of supra soft compact and supra soft Lindel\"{o}f spaces are preserved under soft $S^\star$-continuous mappings.

Keywords: Supra soft Limit; Supra soft boundary; Supra soft closure; Supra soft compact; Almost supra softcompact and mildly supra soft compact.