DefinitionLet S = {0,1}. Then T = is a topology on S, and the resulting topological space is calledSierpinski space.

- S is an inaccessible Kolmogorov space; i.e. S satisfies the T
_{0}axiom, but not the T_{1}axiom. - A topological space is Kolmogorov if and only if it is homeomorphic to a subspace of a power of S.
- For any topological space
*X*with topology*T*, let C(*X*,S) denote the set of all continuous maps from*X*to S, and for each subset*A*of*X*, let I(*A*) denote the indicator function of*A*. Then the mapping*f*:*T*→ C(*X*,S) defined by*f*(*U*) = I(*U*) is a bijective correspondence. - If
*X*is a topological space with topology*T*, then the weak topology on*X*generated by C(*X*,S) coincides with*T*.