Slightly β-continuous functions - Takashi Noiri (International Journal of Mathematics and Mathematical Sciences)
We define a function f:X→Y to be slightly β-continuous if for every clopen set V of Y, f−1(V)⊂Cl(Int(Cl(f−1(V)))). We obtain several properties of such a function. Especially, we define the notion of ultra-regularizations of a topology and obtain interesting characterizations of slightly β-continuous functions by using it.