Integer Reciprocal Space is Topological Space

Theorem
Let $\left({\R, \tau_d}\right)$ be the real number line $\R$ under the usual (Euclidean) topology $\tau_d$.

Let $A \subseteq \R$ be the set of all points on $\R$ defined as:
 * $A := \left\{{\dfrac 1 n : n \in \Z_{>0}}\right\}$

Then the integer reciprocal space $\left({A, \tau_d}\right)$ is a topological space.

Proof
We have that $A \subseteq \R$.

By definition, $\left({A, \tau_d}\right)$ is a subspace of $\left({\R, \tau_d}\right)$.

Hence the result from Topological Subspace is Topological Space.