Published online by Cambridge University Press: 09 April 2009
If we consider any particular topological semigroup S it may seem reasonable to ask for a characterization of all additions on S which make it a topological semiring. We are interested here in this problem when
(i) S is an (I)-semigroup;
(ii) S is [0, ∞) and the multiplication on S is such that 0 and 1 are Zero and identity respectively.