4.1 Topology, topological spaces
Abstracting away from metrics, a topological space is a set, with a collection of so-called open subsets U, satisfying the following properties. We have already seen them, for sequentially open subsets of a metric space, in Proposition 3.2.7.
Definition 4.1.1 (Topology) Let X be a set. A topology on X is a collection of subsets of X, called the opens of the topology, such that:
A topological space is a pair (X, ), where is a topology on X.