The classical Nash Theorem, widely used in economics, political science, and many other fields, is fundamentally based on the Brouwer Fixed Point Theorem, which is a result in pure topology.

Thank you very much Prof. Taras Radul

John Nash won the Nobel prize in Economics for proving the Nash Equilibrium exist in a general class of games. The Nash equilibrium was proved Nash by using the Kakutani fixed point theorem - a generalization of the Brouwer fixed point theorem to set valued functions. In fact fixed point theorems mostly based on topological arguments are very important in applications involving nonlinearities.

https://onlinelibrary.wiley.com/doi/toc/10.1155/9303.si.575812#:~:text=In%20particular%2C%20fixed%20point%20techniques,%2C%20image%20processing%2C%20and%20economics.

Dear Prof.Truman Prevatt,

Thank you very much for your answer. This is very useful and helpful information.

Yes, point-set topology can be used metaphorically to explain socio-political phenomena like espionage, alliances, or domination. Concepts from topology, such as "open sets," "closed sets," and "neighborhoods," can be analogous to social networks and relationships:

Using these topological concepts, one can create models to analyze and visualize complex socio-political interactions and dynamics.