Double Intuitionistic Open Sets with Some Applications

The purpose of this work is to presents a new class of open sets namely Double intuitionistic open sets. The relationships between the Double intuitionistic open and the Double intuitionistic sets are studied including the Double intuitionistic interior set, Double intuitionistic closure set and Double intuitionistic limit point in Double intuitionistic topological spaces were presented and various examples and many observations were presented for each concept, also the definitions of the paired set were presented in general topological spaces Therefore, we generalize it to the Double intuitionistic topological spaces with the presentation of the basic theorem of this new space, and many of the basic characteristics and properties related to these concepts that are presented in the third section as evidence with many examples, taking into account that the opposite is not true for each evidence for these characteristics, which was presented and what we note in the fourth section.