A topological space (M, TM) with the set of all MP-filters as its basis on an R0-algebra M is introduced. Characterizations of differentiate, closure and interior operators in (M, TM) are obtained. It is proved that (M, TM) is connected and covering-compact and satisfies the first separation axiom, and it satisfies the second separation axiom if and only if the set of all principle filters is countable. However, (M, TM) is neither T1 nor regular. It is also proved that (M, TM) is T0 if and only if the R0-algebra M reduces to a Boolean algebra. Finally, product spaces on product R0-algebras are investigated.