Definition:Topology/Definition 1

Definition
Let $S$ be a set such that $S \ne \O$.

A topology on $S$ is a subset $\tau \subseteq \powerset S$ of the power set of $S$ that satisfies the open set axioms:

If $\tau$ is a topology on $S$, then $\struct {S, \tau}$ is called a topological space.

The elements of $\tau$ are called the open sets of $\struct {S, \tau}$.

Also see

 * Equivalence of Definitions of Topology