Let X be a set, and let B be a collection of subsets of X. Then B is basis if:
1.
For all x in X, there exists a B in B such that x is in B
2.
If B1 and B2 are members of B and x is in the intersection of B1 and B2, then there exists a B3 in B completely contained in the intersection of B1 amd B2
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