Theta topological groups (Q690403)

A function \(f\) mapping the topological space \(X\) to the topological space \(Y\) is said to be theta continuous if for each neighbourhood \(V\) of \(f(x)\) with \(x \in X\) there is a neighbourhood \(U\) of \(x\) with \(f(\overline{U}) \subseteq \overline{V}\). This notion is weaker than continuity, but coincides with continuity for regular topological spaces. The notion of a theta topological group is defined in the obvious way. The paper establishes some basic properties of such objects, and provides some examples.