Definition:Michael's Product Topology

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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

  • Results about Michael's product topology can be found here.

Source of Name

This entry was named for Ernest Arthur Michael.