Topological space

A topological space is a pair (X, T), where X is a set, and T is a collection of subsets of X that satisfy the following 3 axioms:

1. The empty set and X are elements of T.
2. The union of any collection of elements in T is in T.
3. The intersection of any finite collection of elements in T is in T.

Elements in T are called "open sets".