topology

Let \(X\) be a set.

A topology \(\mathcal{T}\) on \(X\) is a collection of subsets - each called an open set - such that:

1. Openness of a finite intersection of open sets
2. Openness of a union of open sets

Note that \(\emptyset, X \in \mathcal{T}\), either by definition or by convention of intersection and union (cf. triviale Mengen in einer Topologie)