Any T0 space embeds in a product of copies of the Sierpinski space. #
Prop with the Sierpinski topology. If
X is a topological space, there is a
Opens X → Prop which is the product of the maps
X → Prop given by
x ↦ x ∈ u.
The continuous map from
X to the product of copies of the Sierpinski space, (one copy for each
u coordinate of
productOfMemOpens x is given by
x ∈ u.