Some sandwich type near-rings (Q1287055)

Let \(X\) be a topological space, \((G,+)\) a topological group and fix a continuous function \(\alpha\) from \(G\) into \(X\). Denote by \(N(X,G,\alpha)\) the nearring of all continuous functions from \(X\) to \(G\) under pointwise addition and where the product \(fg\) of two elements \(f,g\in N(X,G,\alpha)\) is defined by \(fg=f\circ\alpha\circ g\). Such a nearring is referred to as a sandwich nearring with sandwich function \(\alpha\). These nearrings have been investigated by various authors. The present author investigates nearrings of this type where the functions satisfy conditions other than continuity.