EDB — 0M1

[0M1] Prerequisites:Generated topology [0J1]↺↻, [0KX]↺↻, [0KZ]↺↻.Let’s resume [0KZ]↺↻. Let again $X$ be a set and $\mathcal{B}$ a family of subsets that satisfy the above properties (a),(b) seen in [0KX]↺↻; suppose $𝜏$ the smallest topology that contains $\mathcal{B}$. Prove that $\mathcal{B}$ is a base for $𝜏$.

We can therefore say that a family that satisfies (a),(b) is a base for the topology it generates. This answers the question posed in [0KV]↺↻.