On certain missing links in the hierarchy of some compact-like covering properties

Abstract

It is found in the literature that several compact-like covering properties have been introduced and studied by different researchers. However, there are certain missing links in the implication-diagram among all these. The aim of this paper is to fill up these gaps by introducing three new types of covering properties in terms of semiopen and preopen sets, thereby providing a balanced and complete diagram in respect of the hierarchy of the existing and the introduced types of properties. The latter types of covering properties are characterized, and studied to some extent, and a number of non-trivial examples are given to justify non-implications. Finally, certain conditions are worked out under which such reverse implications may hold.