On \(\theta\)-generalized closed sets
A subset \(A\) of a topological space \(X\) is called \(\theta\)-closed, if \(A=\text{cl}_\theta (A)\) where \(\text{cl}_\theta(A)= \{x\in X: \text{cl} (U)\cap A\neq\emptyset\) for each open neighbourhood \(U\) of \(x\}\). In this paper the authors consider a new class of subsets, namely \(\theta\)-generalized closed sets, i.e. subsets \(A\) where \(\text{cl}_\theta (A) \subseteq U\) whenever \(A\subseteq U\) and \(U\) is open. They establish basic properties of this class of subsets, in particular they point out that this class is placed properly between the classes of generalized closed sets (in the sense of Levine) and \(\theta\)-closed sets. In the subsequent sections of the paper, \(\theta\)-\(g\)-continuous and \(\theta\)-\(g\)-irresolute functions are introduced and investigated. Moreover, the property ``TGO-connected'' is introduced and the behaviour of this type of connectedness under various mappings is exhibited.
scientific article; zbMATH DE number 1334830