# 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.

Some sources do not hyphenate sub-basis but instead render it as subbasis.

Some sources use the term sub-base (or subbase).

## Linguistic Note

The plural of sub-basis is sub-bases.

This is properly pronounced sub-bay-seez, rather than sub-bay-siz, deriving as it does from the Greek plural form of nouns ending -is.