This paper is a contribution to formal ontology study: the problem of atypical entities. Some individual entities are attached to classes when they do not check all the properties of the class. We introduce the topological operators of interior, border, closure and exterior. These operators allow us to describe whether an entity belonging to a class is typical or not. We define a system of relations of inclusion and membership by adapting the topological operators, based on a precise axiomatic. In this paper, we propose to better formalize these topological relations of inclusion and membership based on the mathematical properties of topological operators. However, there are properties of combining operators of interior, border, closure and exterior allowing the definition of an algebra. We propose to use these mathematical properties as a set of axioms. This set of axioms allows us to establish properties of relations of topological inclusion and membership.