| Abstract: | Given any cancellative continuous semigroup operation $$star $$ on the positive real numbers $$mathbf {R}_+$$ with the ordinary topology, we completely characterize the set $$mathcal {D}_star (mathbf {R}_+)$$ of all cancellative continuous semigroup operations on $$mathbf {R}_+$$ which are distributed by $$star $$ in terms of homeomorphism. As a consequence, we show that an arbitrary semigroup operation in $$mathcal {D}_star (mathbf {R}_+)$$ is homeomorphically isomorphic to the ordinary addition $$+$$ on $$mathbf {R}_+$$. |
