Functional Analysis/Harmonic Analysis/Section 1 Exercises

1) Give as many examples as you can of topological groups which do not fall within any of the examples we gave in section Functional Analysis 9.1.

2) Prove that the inverse of an isomorphism.

3) show that for each $$ x \in G$$ the maps $$ L_x(y) = xy$$ and $$ R_x(y) = yx $$ are topological group homomorphisms.

4)