THE LATTICE OF ORDINARY SMOOTH TOPOLOGIES Cheong, Min-Seok; Chae, Gab-Byung; Hur, Kul; Kim, Sang-Mok;
Lim et al.  introduce the notion of ordinary smooth topologies by considering the gradation of openness[resp. closedness] of ordinary subsets of X. In this paper, we study a collection of all ordinary smooth topologies on X, say OST(X), in the sense of a lattice. And we prove that OST(X) is a complete lattice.