Space S000028

Irrational numbers

Also known as: Irrationals, Z^Z, Omega to the omega power, Baire space, Baire product, Countable power of a countable discrete space

Let XX be the complement of the rational numbers in R\mathbb{R} with the subspace topology.

This space is homeomorphic to the Baire space ωω\omega^\omega with the product topology.

Defined as counterexample #31 ("The Irrational Numbers") in DOI 10.1007/978-1-4612-6290-9. Also defined as counterexample #102 ("ZZ\mathbb{Z}^{\mathbb{Z}}") in DOI 10.1007/978-1-4612-6290-9.