basis

(noun): A physical base or foundation.
(noun): A starting point, base or foundation for an argument or hypothesis.
(noun): An underlying condition or circumstance.
(noun): A regular frequency.
(noun): In a vector space, a linearly independent set of vectors spanning the whole vector space.
(noun): Amount paid for an investment, including commissions and other expenses.
(noun): 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.

Cars must be checked on a yearly basis.
The collection of all possible unions of basis elements of a basis is said to be the topology generated by that basis.