Inverse of Composition of Subsets of Topological Group

Theorem

Let $\struct {G, \odot, \tau}$ be a topological group.

Let $A, B \subseteq G$.

Then:

$\paren {A \odot B}^{-1} = B^{-1} \odot A^{-1}$

Proof

The proof is identical to Inverse of Product of Subsets of Group.

$\blacksquare$

Sources

• 2014: Loukas Grafakos: Classical Fourier Analysis (3rd ed.) ... (previous) ... (next): $1.1.2$: Examples of Topological Groups