Bicompletion of quasi-bitopological near-rings and quasi-bitopological \(N\)-groups (Q1283632)

A distributive nearring \(N\) with a topology \(T\) is called quasi-topological if the mappings \((x,y)\mapsto x+y\), \(x\mapsto ax\), \(x\mapsto xa\), \(a\in N\), are all continuous. It is shown that \((N,-T)\) is a quasi-topological nearring as well. The author likes to call the triple \((N,T,-T)\) a quasi-bitopological nearring. The aim is to carry over some results for quasi-topological groups to quasi-bitopological nearrings. In particular, uniformities, completion, and (continuous) action on \(N\)-groups are considered.