ABSTRACT
The theory of transformation groups is a beautiful area of topology which has connections with dierent parts of mathematics. Generally speaking, this deals with symmetries (automorphisms) of mathematical objects such as vector spaces, topological spaces, manifolds, cellular complexes, etc. Thus, one studies actions of groups on spaces in this theory. In this section, the rudiments of this theory and some elementary results from its point-set topology are discussed. Connectedness of some topological groups will also be ascertained. We also introduce here a geometric denition of (proper) rigid motion and see the justi-cation for describing the elements of the group SO(n) as rotations of Rn.
