Simplicity of near-rings of continuous functions (Q803254)

Let N(G) denote the near-ring of all continuous selfmaps of a topological group G. In this paper we determine the locally compact topological groups G which have a simple near-ring N(G). It is shown that for a locally compact group G the near-ring N(G) is simple, if and only if G is not of order 2 and either contractible or totally disconnected.