A topological ring of functions and a uniform ring of functions (Q5896495)

By a uniform ring the authors mean a ring with a uniformity having translation-invariant base under addition and multiplication; it is shown that a uniform ring is a topological ring, but the converse is not true. Further, the authors study the set of all mappings \(f:E\to F\) in two cases (i) \(E\) is a nonempty set, \(F\) a topological ring and (ii) \(E\) is a nonempty set and \(F\) a uniform ring.