We shall study topological invariants (compactness, connectedness) of the following Matrix groups:
The orthogonal groups O(n).
The special orthogonal groups SO(n).
The unitary group U(n).
The special unitary Group SU(n).
We will try to understand a proof of the fact that the general linear group over the real field has exactly two connected components.
Metric space and Group action are required.
