Saeid Jafari

On some low separation axioms via &- open and &- closure operator

In this paper, we introduce and study two new low separation axioms called λ-R0 and λ-R1 by using the notions of λ-open sets and λ-closure operator.

Properties of (θ,s)-continuous functions

Abstract Joseph and Kwack [Proc. Amer. Math. Soc. 80 (1980) 341–348] introduced the notion of ( θ , s )-continuous functions in order to investigate S -closed spaces due to Thompson [Proc. Amer. Math. Soc. 60 (1976) 335–338]. In this paper, further properties of ( θ , s )-continuous functions are obtained and relationships between ( θ , s )-continuity, contra-continuity and regular set-connectedness defined by Dontchev et al. [Internat. J. Math. Math. Sci. 19 (1996) 303–310 and elsewhere] are investigated.

On α-quasi-irresolute functions

Joseph and Kwack [9] introduced the notion of (θ,s)-continuous functions in order to investigateS-closed spaces due to Thompson [32]. In [26], the present authors investigated further properties of (θ,s)-continuous functions. In this paper, we introduce a new class of functions called α-quasi-irresolute functions which is weaker than (θ,s)-continuous and improve some results established in [26].

On pre-Λ-Sets and pre-v-Sets

We introduce the notions of a pre-Λ-set and a pre-V-set in a topological space. We study the fundamental properties of pre-Λ-sets and pre-V-sets and investigate the topologies defined by these families of sets.

On semi-g-regular and semi-g-normal spaces ⁄

The aim of this paper is to introduce and study two new classes of spaces, called semi-g-regular and semi-g-normal spaces. Semi-g-regularity and semi-g-normality are separation properties obtained by utilizing semi-generalized closed sets. Recall that a subset A of a topological space (X;?) is called semi-generalized closed, briefly sg-closed, if the semi-closure of A µ X is a subset of U µ X whenever A is a subset of U and U is semi-open in (X;?) .

ON SOME NEW MAXIMAL AND MINIMAL SETS VIA θ-OPEN SETS

Abstract. Nakaoka and Oda ([1] and [2]) introduced the notion of max-imal open sets and minimal closed sets in topological spaces. In thispaper, we introduce new classes of sets called maximal θ -open sets, min-imal θ -closed sets, θ -semi maximal open and θ -semi minimal closed andinvestigate some of their fundamental properties. 1. Introduction and preliminariesGeneralized open sets play a very important role in General Topology andthey are now the research topics of many topologists worldwide. Indeed asignificant theme in General Topology and Real Analysis concerns the variouslymodified forms of continuity, separation axioms etc by utilizing generalizedopen sets. One of the most well-known notions and also an inspiration sourceis the notion of θ -open sets introduced by N. V. Veli˘cko [3] in 1968. Since thecollection of θ -open sets in a topological space ( X,τ ) forms a topology τ θ on X then the union of two θ -open sets is of course θ -open. Moreover τ = τ θ if andonly if ( X,τ ) is regular.F. Nakaoka and N. Oda in [1] and [2] introduced the notion of maximal opensets and minimal closed sets. The purpose of the present paper is to introducethe concept of a new class of open sets called maximal

Characterizations of ΛΘ-R0and ΛΘ- R1topological spaces

We introduce and study two new weak separation axioms called ΛΘ-R0 and ΛΘ-R1 by using the notions of (Λ,Θ)-open sets and (Λ,Θ)-closure operators.

Characterizations of ΛΘ-R0 and ΛΘ-R1 topological spaces

We introduce and study two new weak separation axioms called ΛΘ-R0 and ΛΘ-R1 by using the notions of (Λ,Θ)-open sets and (Λ,Θ)-closure operators.

ON ALMOST PRECONTINUOUS FUNCTIONS

Nasef and Noiri (1997) introduced and investigated the class of almost precon- tinuous functions. In this paper, we further investigate some properties of these functions.

On strongly faint e-continuous functions

A new class of functions, called strongly faint e-continuous function, has been defined and studied. Relationships among strongly faint e-continuous functions and econnected spaces, e-normal spaces and e-compact spaces are investigated. Furthermore, the relationships between strongly faint e-continuous functions and graphs are also investigated.