Definition:Michael's Product Topology

Definition
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.

Also see

 * Michael's Product Topology