Various Types of Supra Pre-compact and Supra Pre-Lindelöf Spaces

The purpose of this article is to introduce three types of supra compactness and three types of supra Lindelofness via supra topological spaces based on the supra pre-open sets. With the help of examples, we illustrate the relationships among them and show their relationships with some kinds of supra compactness and supra Lindelofness given in [3]. We characterize each type of space and investigate the image of them under pre-irresolute mappings. Also, we prove that these spaces are preserved under the finite product spaces, and give a sufficient condition for the equivalence among supra compact, almost supra compact and supra pre-compact spaces. At the end of each section, we provide some examples to demonstrate that the spaces studied and their counterparts, introduced in [9], are independent of each other.