On Double Topological Structures

Topological spaces are mathematical structures that allow the formal definition of concepts such as convergence, connectedness, continuity, proximity, uniformity, and syntopogenous structures. They appear in virtually every branch of modern mathematics and are a central unifying notion. The branch of mathematics that studies topological spaces in their own right is called topology. The notions of fuzzy sets and intuitionistic fuzzy sets used to generalize the topological spaces. Recently, Garcia and Rodabaugh could end some doubts around the term "intuitionistic" by giving it the new name "double". Since that time, the new term is used to study the topological notions.