Abstract

In this paper, we use r-open sets to introduce the concept of weakly r-supercontinuous functions. Then, basic properties and a number of connections between these functions and other types of generalized continuous functions are examined. A weakly r-supercontinuous function is weaker than -continuous but stronger than weakly continuous. Furthermore, we present some characterizations of weakly r-supercontinuous functions. The last section starts with a comparison between weakly r- supercontinuous functions and some other types of functions when the underlying spaces possess particular topological properties. We end this work by analyzing the composition of weakly r-supercontinuous functions.