  The continued fraction mapping maps a number in the interval $[0,1)$ to the
sequence of its partial quotients. When restricted to the set of irrationals,
which is a subspace of the Euclidean space $\mathbb{R}$, the continued fraction
mapping is a homeomorphism onto the product space $\mathbb{N}^{\mathbb{N}}$,
where $\mathbb{N}$ is a discrete space. In this short note, we examine the
continuity of the continued fraction mapping, addressing both irrational and
rational points of the unit interval.
