Abstract
As applications on infra - beta - open set for new classes of mappings and new concepts topological spaces are introduced, namely, infra-beta-continuous, infra- beta -irresolute, infra- beta -open(closed) mapping, infra - beta - tau i (i = 0, 1, 2, 3, 4), infra - beta - compact and infra - beta - 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 con-cepts and others are discussed and counter examples are given in order to investigate opposite relations.