\begin{definition}[Definition:Michael's Product Topology]
Let $\struct {\R, \tau_d}$ be the real number line with the usual (Euclidean) topology.
Let $\Bbb I := \R \setminus \Q$ denote the set of irrational numbers.
Let $\struct {S, \sigma} := \struct {\R, \tau^*} \times \struct {\Bbb I, \tau'}$, where:
:$\tau^*$ is the discrete irrational extension of $\tau_d$ by $\Bbb I$
:$\tau'$ is the subspace topology on $\Bbb I$ induced by $\tau_d$.
$\struct {S, \sigma}$ is referred to as '''Michael's product topology'''.
\end{definition}