MathGloss

A basis for a topology τ\tau on a set XX is a collection B\mathcal B of subsets of XX such that

  1. All points are contained in at least one element of B\mathcal B, and
  2. If xBB’’x\in B’\cap B’’ then there exists at least one BBB\in \mathcal B such that xBBB’’x\in B \subset B’\cap B’’.