Argumentation of introducing a discrete-continuous topology in the interests of algorithmization of complex functioning processes

The main aim of the research is to show and prove the necessity of introducing a new, discrete-continuous topological structure to describe complicated systems and processes of their functioning. Currently, there are two topological structures: continuous and discrete. At the same time, there are functional approaches in order to describe complicated systems and processes of their functioning, based on continuous topology. Until now, it has not been possible to build full functionality for the design of complicated technical objects. Therefore, the functional approach does not fully correspond to the increasingly complicated tasks of our time. The introduction of discrete-continuous topology is especially important for the exploring and modeling of complicated systems and processes of their functioning. In order to prove this fact, the present study describes the properties of complicated processes using examples of the flight process and the design process. The examination of these processes, as the most complicated, proves that the complicated systems and processes are topological spaces with metric, so they can be represented in the form of an oriented progressively bounded graph. Also, it proves the topological invariants of complicated systems and the processes of functioning. Presentation of the complicated processes in the form of a directed graph allows getting shorter path to their algorithmicization and programming, which is necessary for existing practice. In addition, the presentation of a complicated process as a directed graph will allow using the apparatus of graph theory for such purpose and will significantly expand the capabilities of programmers.