Axiom:Open Set Axioms

Definition
Let $S$ be a set.

The open set axioms are the conditions under which elements of a subset $\tau \subseteq \powerset S$ of the power set of $S$ need to satisfy in order to be open sets of the topology $\tau$ on $S$:

Also see

 * Empty Set is Element of Topology, which demonstrates that it is not necessary to specify that $\O \in \tau$ as this follows directly from the axioms.
 * Axiom:Closed Set Axioms