In this paper a modeling formalization based on topological functioning model (TFM) is proposed. TFM uses mathematical foundations that holistically represent complete functionality of the problem and application domains. With the TFM we can do formal analysis of a business system and also enable textual functional requirement checking, missing requirement checking in conformance with the problem domain. After construction of the TFM a domain object model is defined by performing TFM transformation. Using TFM and constructed domain object model it is possible to introduce more formalism in the unified modeling language (UML) diagrams and in their construction. In this paper we have transformed topology from the TFM to the UML class diagrams. By using TFM and topological class diagrams it is possible to define business logic layer, traceability and model driven architecture (MDA) model transformation. This research can be considered to be a step towards the completeness of the MDA.