*Definition [#s8181c9e]
-A subset U of X is called β-open if U ⊂ cl(int(cl(U))).

*Reference [#r9e3ac18]
-Basu, C. K.; Afsan, B. M. Uzzal; Ghosh, M. K., ''A class of functions and separation axioms with respect to an operation.'' (English summary), Hacet. J. Math. Stat. 38 (2009), no. 2, 103-118.