basis

ot noun

1. A regular frequency. Cars must be checked on a yearly basis.
2. A collection of subsets ("basis elements") of a set, such that this collection covers the set, and for any two basis elements which both contain an element of the set, there is a third basis element contained in the intersection of the first two, which also contains that element. The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.
3. A physical base or foundation.
4. A starting point, base or foundation for an argument or hypothesis.