Considering a transformation semigroup with finite height we define the notion of indicator sequence in such a way that any two transformation semigroups with the same indicator sequence have the same height. Also related to any transformation semigroup a topological space, called indicator topological space, is defined in such a way that transformation semigroups with homeomorphic indicator topological spaces have the same height. Moreover any two transformation semigroups with homeomorphic indicator topological spaces and finite height have the same indicator sequences.