Definition:Inverse of Subset of Topological Group

Definition

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

Let $A \subseteq G$.

We define the inverse $A^{-1}$ of $A$ by:

$A^{-1} = \set {a^{-1} : a \in A}$

where $a^{-1}$ denotes the inverse element of $a \in G$.

Sources

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