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...

D. Molodtsov (1999) [1] introduced the concept of a soft set as a new approach for modeling uncertainties. Xiao et al. [7] and Pei and Miao [8] discussed the relationship between soft sets and information systems. They showed that soft sets are a class of special information systems. So it’s important to study the structures of soft sets for information systems. Shabir and Naz(2011) [20], studi...

The purpose of this paper is to introduce new separation axioms semi*-regular, semi*-normal, s*regular, s**-normal using semi*-open sets and investigate their properties. We also study the relationships among themselves and with known axioms regular, normal, semi-regular and semi-normal. Mathematics Subject Classification 2010: 54D10, 54D15

we study interior operators and interior structures in a fuzzy setting.we investigate systems of “almost open” fuzzy sets and the relationshipsto fuzzy interior operators and fuzzy interior systems.

The concepts of fuzzy θ-open (θ-closed)sets and fuzzy θ-closure operator are introduced and discussed in intuitionistic fuzzy topological spaces. As applications of these concepts, certain functions are characterized in terms of intuitionistic fuzzy θ-closure operator.

For a closure space (P,φ) with φ(∅) = ∅, the closures of open subsets of P , called the regular closed subsets, form an ortholattice Reg(P,φ), extending the poset Clop(P,φ) of all clopen subsets. If (P,φ) is a finite convex geometry, then Reg(P, φ) is pseudocomplemented. The Dedekind-MacNeille completion of the poset of regions of any central hyperplane arrangement can be obtained in this way, ...