There is a general agreement that problems which are highly complex in any naive sense are also difficult from the computational point of view. It is therefore of great interest to find invariants and invariant structures which measure in some respect the complexity of the given problem. One of the basic problems of Topology is to determine when two given geometric objects are homeomorphic. This can be quite difficult in general. Our first goal will be to define exactly what the geometric objects are that one studies in Topology. These are called topological spaces. The set of invariants is proven to be necessary and sufficient to characterize topological equivalence classes of binary relations between simple letters.