Zero is not Condensation Point of Integer Reciprocal Space Union with Closed Interval

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

Let $\left({A, \tau_d}\right)$ be the integer reciprocal space under the usual (Euclidean) topology.

Let $B$ be the uncountable set:
 * $B := A \cup \left[{2 \,.\,.\, 3}\right]$

where $\left[{2 \,.\,.\, 3}\right]$ is a closed interval of $\R$.

$2$ and $3$ are to all intents arbitrary, but convenient.

Then $0$ is not a condensation point of $B$ in $\R$.

Proof
Let $I$ be an open set of $\R$ which contains $0$.

Then $I$ is a of the form:
 * $I := \left({- a \,.\,.\, b}\right) \subseteq \R$

From Zero is Omega-Accumulation Point of Integer Reciprocal Space Union with Closed Interval, there is a countably infinite number of points of $B$ in $I$.

However, when $b < 2$ there is not an uncountable number of points of $B$ in $I$.