In this paper a problem domain and system static modeling formalization approach and formalization of static models based on topology borrowed from topological functioning model (TFM) is proposed. TFM uses mathematical foundations that holistically represent complete functionality of the problem and application domains. With the application of TFM within software development process it is possible to do formal analysis of a business system and in a formal way model static structure of the system. Software development starts with construction of TFM of a system functioning, after what the constructed TFM is transformed into problem domain object model. By doing further transformations of TFM it is possible to introduce more formalism in the Unified Modeling Language (UML) diagrams, their construction and in software development process. In this paper topology is introduced into the UML class diagrams and is defined approach for developing topological class diagrams.