Basic topological structures of the theory of ordinary differential equations

Abstract

If you open any book on the theory of ordinary differential equations (TODE) you can observe that almost every proof in the TODE uses the continuity of the dependence of a solution of the Cauchy problem on initial data and parameters of the right-hand side. But the classical TODE has few theorems assuring this continuity. In general they suppose the continuity of the right-hand side. We can note a trivial