Definition:Sub-Basis/Synthetic Sub-Basis

Definition
Let $X$ be a set.

A synthetic sub-basis on $X$ is any subset $\mathcal S \subseteq \mathcal P \left({X}\right)$ of the power set of $X$.

Also known as
Some sources do not distinguish between a synthetic sub-basis and an analytic sub-basis, and instead use the definition for an analytic sub-basis and just call that a sub-basis.

Also see

 * Definition:Topology Generated by Synthetic Sub-Basis
 * Definition:Analytic Sub-Basis
 * Definition:Basis (Topology)


 * Synthetic Basis formed from Synthetic Sub-Basis