In , Açıkgöz et al. introduced and investigated the notions of w-I-continuous and w*-I-continuous functions in ideal topological spaces. In this paper, we investigate their relationships with continuous and θ-continuous functions.
We define a multifunction F: X ⇝ Y to be upper (lower) D*-supercontinuous if F+(V) (F−(V)) is d*-open in X for every open set V of Y. We obtain some characterizations and several properties concerning upper (lower) D*-supercontinuous multifunctions.
An ideal on a set X is a nonempty collection of subsets of X with heredity property which is also closed under finite unions. The concept of generalized closed sets in bitopological
spaces was introduced by Sundaram. In this paper, we introduce and study the concept of generalized closed sets with respect
to an ideal in an ideal bitopological space.
We introduce a new notion called contra-(μ,λ)-continuous functions as functions on generalized topological spaces . We obtain some characterizations and several properties of such functions. The functions enable us to formulate a unified theory of several modifications of contra-continuity due to Dontchev .
A definition of a generalized quotient topology is given and some characterizations of this concept, up to generalized homeomorphisms, are furnished. For the first approach, we exhibit a monotonic map spanning that generalized quotient topology. We also prove that the notions of generalized normality and generalized compactness are preserved by those quotient structures.
A new kind of sets called generalized μ-closed (briefly g μ-closed) sets are introduced and studied in a topological space by using the concept of generalized open sets introduced by Á. Császár. The class of all g μ-closed sets is strictly larger than the class of all μ-closed sets. Furthermore, g-closed sets (in the sense of N. Levine ) is a special type of g μ-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of μg-regular and μg-normal spaces have been given.
A new kind of sets called generalized w-closed (briefly gw-closed) sets is introduced and studied in a topological space by using the concept of weak structures introduced by Á. Császár in . The class of all gw-closed sets is strictly larger than the class of all w-closed sets. Furthermore, g-closed sets (in the sense of N. Levine ) is a special type of gw-closed sets in a topological space. Some of their properties are investigated. Finally, some characterizations of w-regular and w-normal spaces have been given.
We introduce and investigate R-M-continuous functions defined between sets satisfying some minimal conditions. The functions enable us to formulate a unified
theory of modifications of R-continuity : R-irresoluteness , R-preirresoluteness .
The purpose of this paper is to introduce ideal minimal spaces and to investigate the relationships between minimal spaces
and ideal minimal spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and
characterizations related to these sets are given.