The rational world and the rational Urysohn space
Peter Cameron
The set Q of rational numbers is obviously an interesting topological space. In 1920, Waclaw Sierpiński gave a lovely characterisation of it. The simplest way to state it is to say that a countable, metrisable, space without isolated points is homeomorphic to Q. (Sierpiński also gave a purely topological characterisation: a countable, second countable, 0-dimensional, T1 topological space without isolated points is homeomorphic to Q.)
In 1985, Peter Neumann named this topological space the...