In this paper, it is proved that if (X, T ) is a topological space, then the collection of all semi-open sets A in (X, T ) such that A ∩ B is semi-open for every semi-open set B in (X, T ) is a topology on X and that this topology is finer than the topology F (T ) constructed by S. Crossley in [1]. The π-relationship between these topologies is established. Characterizations of semi-continuous and irresolute maps are presented in terms of semi-limit and semi-closure.