up:: Topological Space
The Sierpiński Space is defined over a set with two elements, with the Topology that only one of those is an open set (the other, thus, is closed).
Formally, it is the set whose topology is .
Properties
Through the Sierpiński space, one can prove that Every topology has a bijection with the Hom-Set of its continuous functions to the Sierpiński space: that is, given a topology, each open set has an associated continuous function which “picks it out” from the Sierpiński’s space non-trivial open set.