Grill v- Space

Abstract

This scientific study aims to introduce a new type of topological space, called "Grill v-space", with the aim of contributing to scientific knowledge in this field. New generalizations were developed for both the local function and the Kuratowski closure function in order to generalize their concepts. Subsequently, these generalizations were used to define a new topology based on the concepts associated with the grill and the v -space. The set of v -open in v -space is defined as the sum of the set of v -open forms in v -space when the grill consists of the subsets of P(X) except the empty set. Many of the properties of this new space were demonstrated, and a number of illustrative examples were given.