# Continuous group

In the fundamental works on the theory of Lie groups (S. Lie, H. Poincaré, E. Cartan, H. Weyl, and others) it is a group of smooth or analytic transformations of the space $\mathbf R^n$ or $\mathbf C^n$, depending smoothly or analytically on parameters. When there are finitely many numerical parameters, a continuous group is called finite, which corresponds to the modern concept of a finite-dimensional Lie group. In the presence of parameters that are functions one speaks of an infinite continuous group, which corresponds to the modern concept of a pseudo-group of transformations. Nowadays (1988) the term "continuous group" often stands for topological group [2].