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Abstract
First, we introduce the notion of f I-sets and investigate their properties in ideal topological spaces. Then, we also introduce the notions of R I C-continuous, f I-continuous and contra*-continuous functions and we show that a function f: (X,τ,I) to (Y,ϕ) is R I C -continuous if and only if it is f I-continuous and contra*-continuous.
Summary In [6] we introduced and investigated the notions of f I -sets and f I -continuous functions in ideal topological spaces. In this paper, we investigate their further important properties.
Abstract
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.
Abstract
In 1986, Tong [13] proved that a function f : (X,τ)→(Y,ϕ) is continuous if and only if it is α-continuous and A-continuous. We extend this decomposition of continuity in terms of ideals. First, we introduce the notions of regular-I-closed sets, A I-sets and A I -continuous functions in ideal topological spaces and investigate their properties. Then, we show that a function f : (X,τ,I)→(Y, ϕ) is continuous if and only if it is α-I-continuous and A I-continuous.
Summary
We introduce the notion of a semi-I-regular set and investigate some of its properties. We show that it is weaker than the notion of a regular-I-closed set. Additionally, we also introduce the notion of an AB I -set by using the semi-I-regular set and study some of its properties. We conclude that a subset A of an ideal topological space (X,τ,I) is open if and only if it is an AB I -set and a pre-I-open set.
Abstract
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.
. [2] Dontchev , J. , Ganster , M. , Noiri , T. 1999 Unified operation approach of generalized closed sets via topological ideals Math. Japan 49 395 – 401 . [3