Meaning

• A physical base or foundation.

• A starting point, base or foundation for an argument or hypothesis.

• An underlying condition or circumstance.

• A regular frequency.

  "Cars must be checked on a yearly basis."

• In a vector space, a linearly independent set of vectors spanning the whole vector space.

• Amount paid for an investment, including commissions and other expenses.

• 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."