RUDN Journal of Engineering ResearchRUDN Journal of Engineering Research2312-81432312-8151Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)3029410.22363/2312-8143-2021-22-3-270-282Research ArticleArgumentation of introducing a discrete-continuous topology in the interests of algorithmization of complex functioning processesMalininaNatalia L.<p>Candidate of Physical and Mathematical Sciences, Associate Professor of the Department 604, Aerospace Faculty</p>malinina806@gmail.comhttps://orcid.org/0000-0003-0116-5889Moscow Aviation Institute (National Research University)3012202122327028224022022Copyright © 2021, Malinina N.L.2021<p style="text-align: justify;">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.</p>complicated processdiscrete-continuous topologymodelgraph theoryсложный процессдискретно-непрерывная топологиямодельтеория графов[Kelley DL. General topology. New York, Toronto, London: D. van Nostrand Company, Inc.; 1955.][Kuratovski K, Mostovski A. Set theory. Amsterdam, Warsaw: North-Holland Publishing Company; 1968.][Viro OYa, Ivanov OA, Netsvetaev NYu, Kharlamov VM. Elementary topology. Problem textbook. AMS; 2008.][Korukhov VV. The model of discrete-continuous space-time and motion paradoxes “Achilles” and “Dichotomy.” Philosophy of Sciences. 2001;(2(10)):4. (In Russ.)][Korukhov VV, Sharipov ОV. The structure of space-time and the physical vacuum problem: modern status and future trends. Philosophy of Sciences. 2006;(1(28)): 20–36. (In Russ.)][Chorafas DN. Systems and simulation. 1st ed. Academic Press; 1965.][Quade ES. Analysis for military decisions. Santa Monica: RAND Corporation, 1964.][Malinina NL. Mathematical aspects of the design process. Applied geometry, engineering graphics, computer design. 2006;(3(5)):12–18.][Hill PH. The science of engeneering design. New York: Tufts University, Holt, Rinehart and Winston, Inc.; 1970.][Moiseev N. Mathematics sets up an experiment. Moscow: Nauka Publ.; 1979. (In Russ.)][Malinina NL, Malinin LI. Topological properties of the design process. Trudy MAI. 2008;(30):3. (In Russ.)][Malinin LI, Malinina NL. Graph isomorphism in theorems and algorithms. Moscow: URSS Publ.; 2009. (In Russ.)][Berge C. The theory of graphs and its applications. London: Methuen; New York: Wiley; 1962.][Ore О. Theory of graphs. Providence: American Mathematical Society; 1962.][Chinn WG, Steenrod NE. First concepts of topology: the geometry of mappings of segments, curves, circles, and disks. Washington: Mathematical Association of America; 1966. https://doi.org/10.5948/UPO9780883859339][Markov AA, Nagorny NM. Theory of algorithms. Dordrecht, Boston, London: Kluwer Academic Publishers, 1988.]