The present paper, some well-known theorems have been improved, such as a proof of one theorem and the inverse direction of another theorem in the fuzzifying topological space and the fuzzifying bitopological space. We prove one theorem by use less conditions in the fuzzifying topological space and the fuzzifying bitopological space. Also, we prove the equivalent definition of semi open sets in the fuzzifying topological space and the fuzzifying bitopological space. Additionally, the equivalent definition of the closure operator in the fuzzifying topological space and the fuzzifying bitopological space has been also proved. Finally, some supporting examples are provided.