As applications on inf ra open set for new classes of mappings and new concepts topological spaces are introduced, namely, infra- continuous, inf ra irresolute, inf ra open(closed) mapping, inf ra i (i = 0; 1; 2; 3; 4), inf ra compact and inf ra connected space. Some of special results and properties which belong to these various applications are established and studied. Moreover, the relations and opposite relations between these new concepts and others are discussed and counter examples are given in order to investigate opposite relations.