Regular open sets in fuzzifying topology redefined

In 2000 [1], Zahran introduced the concept of regular open sets in fuzzifying topology. In 2004 [2], Sayed and Zahran, gave an example to illustrate that the statements:(1)⊨A∈Rτ→A∈τ⊨A∈Rτ→A∈τ (Lemma 2.2 [1]); and(2)⊨(A∈Rτ∧B∈Rτ)→A∩B∈Rτ⊨(A∈Rτ∧B∈Rτ)→A∩B∈Rτ (Theorem 2.4 [1]),are incorrect. In the present paper we redefine this concept to make these statements correct. Furthermore, by making use of our definition of regular open sets, the concepts of almost continuity and δ-continuity are introduced and studied in fuzzifying topology.