Topology

Let X be any set and let T be a family of subsets of X. Then T is a topology on X if
- both the empty set and X are elements of T,
- any union of elements of T is an element of T, and
- any intersection of finitely many elements of T is an element of T.
If T is a topology on X, then X together with T is called a topological space.

Example:
X = {a,b,c} is a set.
T = {0, {a,b,c}, {a,b}, {a,c}, {b,c}. {a}, {b}, {c} } is a family of subsets.
[X, T] is a topological space.

From "Topology Without Tears" by

Sidney A. Morris.