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]↺↻.