In this chapter, some basic operations on the bipolar intuitionistic fuzzy soft set structure are redefined. The redefined union, intersection, and, or, empty set, absolute set, complement, subset operations on bipolar intuitionistic fuzzy soft set structure are supported with examples. Then the concept of bipolar intuitionistic fuzzy soft topology is defined. Important concepts such as interior, closure in bipolar intuitionistic fuzzy soft topological spaces are examined and necessary theorems are proved. Finally, an application is made using TOPSIS on financial performance evaluation among banks using the defined bipolar intuitionistic fuzzy soft topology.