Applications of pre-open sets

Applications of fuzzy $e$-open sets

The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

On Pre-θ-Open Sets and Two Classes of Functions

on pre-θ-open sets and two classes of functions

Remarks on Pre-ℐ-Regular Pre-ℐ-Open Sets

We deal with the new class of pre-ℐ-regular pre-ℐ-open sets in which the notion of pre-ℐ-open set is involved. We characterize these sets and study some of their fundamental properties. We also present other notions called extremally pre-ℐ-disconnectedness, locally pre-ℐ-indiscreetness, and pre-ℐ-regular sets by utilizing the notion of pre-ℐ-open and pre-ℐ-closed sets by which we obtain some eq...

Some Applications of Minimal Open Sets

We characterize minimal open sets in topological spaces. We show that any nonempty subset of a minimal open set is pre-open. As an application of a theory of minimal open sets, we obtain a sufficient condition for a locally finite space to be a preHausdorff space. 2000 Mathematics Subject Classification. 54A05, 54D99.