Basis

From Conservapedia

Basis is a mathematics term.

A basis B for a topology T on a set X is a collection of subsets of X (called basis elements) such that

1. each x in X, is in at least one basis element.
2. if x is in the intersection of 2 basis elements B₁ and B₂, then it is in some basis element B₃, where B₃ is a subset of B₁ ∩ B₂.

If B satisfy the above 2 conditions, then the topology T generated by B is the collection of subsets U of X such that for each x in U, there is a basis element V in B such that x is in V and V is a subset of U.