An invariant ultrametric distance $\omega$ is introduced in the differential algebra $\mathcal H(\mathbb T)$ of generalized hyperfunctions on the unit circle $\mathbb T$ due to the author. For the induced topology, addition and mutiplication are continuous maps. It is also shown that the inversion is a continuous endomorphism of the group $\mathcal H^*(\mathbb T)$ of invertible elements of $\mathcal H(\mathbb T)$. Next, the association of an element in $\mathcal H(\mathbb T)$ with a distribution or an analytic function on $\mathbb T$ is related to its position with respect to the unit ball.