EDB — 0KX

[0KX]Let \({\mathcal B}\) be a base for a topology \(𝜏\) on \(X\); then the following two properties apply.

(a)

\(\underline⋃ {\mathcal B} = X\) that is, the union of all the elements of the base is \(X\).

(b)

Given \(B_ 1,B_ 2∈ {\mathcal B}\) for each \(x∈ B_ 1∩ B_ 2\) there exists \(B_ 3∈ {\mathcal B}\) such that \(x∈ B_ 3⊆ B_ 1∩ B_ 2\).