The main goal of this paper is to introduce and study a new class of function via the notions of $e$-$\theta$-open sets and $e$-$\theta$-closure operator which are defined by Ozkoc and Aslım [10] called weakly $eR$-open functions and $e$-$\theta$-open functions. Moreover, we investigate not only some of their basic properties but also their relationships with other types of already existing topological functions. پرونده مقاله

The aim of this paper is to introduce and obtain some characterizations of weakly $e$-irresolute functions by means of $e$-open sets defined by Ekici [6]. Also, we look into further properties relationships between weak $e$-irresoluteness and separation axioms and completely $e$-closed graphs. پرونده مقاله

‎The main goal of this paper is to introduce and study two new class of functions‎, ‎called weakly $e^*$-irresolute functions and strongly $e^*$-irresolute functions‎, ‎via the notion of $e^*$-open set defined by Ekici [7]. ‎We obtain several fundamental properties and characterizations of these functions‎. ‎Moreover‎, ‎we investigate not only some of their basic properties but also their relationships with other types of already existing topological functions‎. پرونده مقاله

The aim of this paper is to introduce and study two new classes offunctions called weakly $e^{*}$-open functions and weakly$e^{*}$-closed functions via the concept of $e^{*}$-open set definedby Ekici \cite{erd1}. The notions of weakly $e^{*}$-open and weakly$e^{*}$-closed functions are weaker than the notions of weakly$\beta$-open and weakly $\beta$-closed functions defined by Caldasand Navalagi \cite{cal}, respectively. Moreover, we investigate notonly some of their fundamental properties, but also theirrelationships with other types of existing topological functions.‎ پرونده مقاله

‎The main purpose of this paper is to study the class of $e\text{-}\theta$-open sets and explore some of their new properties‎. ‎Also‎, ‎we introduce and study some weak separation axioms by utilizing $e\text{-} \theta$-open sets‎. ‎In addition‎, ‎we define the notion of $e\text{-}\theta\text{-}$kernel and slightly $e\text{-}\theta\text{-}R_0$ spaces‎. ‎Furthermore‎, ‎we apply them to discuss some fundamental properties of the graph functions‎. ‎We obtain not only some characterizations but also many new results‎. پرونده مقاله

‎The main purpose of this paper is to introduce and investigate a new class of open sets called $\delta_e$-open sets‎. For this aim‎, ‎first we define and study the notion of $e$-regular open set via $e$-closure operator‎. ‎Then‎, ‎we introduce the notion of $\delta_e$-open set via $e$-regular open set‎. ‎Several fundamental properties of the notion of $\delta_e$-open set have been revealed‎. ‎Also‎, ‎we show that the family of $\delta_e$-open sets is a topology strictly weaker than $\tau^{\delta}$ and stronger than $\tau$‎. ‎In addition‎, ‎we investigate relationships between the notion of $\delta_e$-open set and other existing notions in topology such as open sets‎, ‎regular open sets and $\delta$-open sets‎. ‎Furthermore‎, ‎we give not only various properties and characterizations but also examples and counterexamples‎. ‎Finally‎, ‎some properties related to separation axioms are revealed‎. پرونده مقاله