The concept of an ideal on a topological space (nowadays called a topological ideal) has played a fundamental role in several of the advances in general topology. In the last century, a large number of works have arisen that have enriched the literature related to the concept of topological ideal. Very recently, topological ideals have again received special attention for their versatility in tackling topology problems and in studying rough set models, as we can see in the references [19], [7], [3], [12], [16], [5], [9], [10]. In 2014, Hatir and Al-Omari [8] introduced the concept of []-local function and studied some of its most relevant properties. The study carried out in [8] served as motivation to define the class of the [][]-I -open sets in [11], which was later used in [14] to introduce new variants of continuous functions, called [][]-I-continuous, weakly []-J -continuous and str...