Ekici, E.Jafari, S.Latif, R.M.2025-01-272025-01-2720101126-8042https://hdl.handle.net/20.500.12428/13889In 1943, Fomin 7 introduced the notion of ?-continuity. In 1966, the notions of ?-open subsets, ?-closed subsets and ?-closure were introduced by Veli?ko 18 for the purpose of studying the important class of H-closed spaces in terms of arbitrary filterbases. He also showed that the collection of ?-open sets in a topological space (X; ?) forms a topology on X denoted by ? ? (see also 12). Dickman and Porter 4, 5, Joseph 11 continued the work of Veli?ko. Noiri and Jafari 15, Caldas et al. 1 and 2, Steiner 16 and Cao et al 3 have also obtained several new and interesting results related to these sets. In this paper, we will off a finer topology on X than ?? by utilizing the new notions of ??-open and ??-closed sets. We will also discuss some of the fundamental properties of such sets and some related maps.eninfo:eu-repo/semantics/closedAccesstopological spacesθ-open setsθ-closed setsωθ-open setsωθ-closed setsanti locally countableωθ-continuityArticle272933042-s2.0-79960251553Q4