ON N-FEEBLY OPEN SET IN TOPOLOGICAL SPACES

Abstract

In this research, the concept of N-feeble-open (N-feeble-O) sets in topological spaces is introduced and studied and the concept of N-feeble-O sets is used to construct a new class of compact spaces. Several fundamental properties of N-feeble-O sets are proved, such as relationships with feeble-open sets, semi-open sets and N-semi-open sets. Topological concepts that are related to this one, including interior, closure, derived sets, adherent points and subspaces, are also explored. A new form of N-feeble compactness is defined, based on the newly introduced N-feeble-O sets, and certain fundamental properties of this compactness are explored. Relationships between the N-feeble compact spaces and other compactness notions, namely, compactness, semi-compactness and feeble compactness, are investigated. A number of theorems, propositions, corollaries and illustrative examples are given to get the results obtained and to clarify the differences between these classes. In addition, preservation properties with subspaces, closed subsets and intersections are explored. The results add to the generalized topological concepts and lay foundations for future research of N-feeble-O sets, compactness and associated topological functions.