\begin{definition}[Definition:Basic Open Set]
Let $T = \struct {S, \tau}$ be a topological space.
Let $\BB \subseteq \tau$ be a basis for $T$.
Let $U \in \BB$.
Then $U$ is a '''basic open set''' of $T$.
That is, a '''basic open set''' of a topology is an open set of that topology which is an element of a basis for that topology.
The basis itself needs to be specified for this definition to make sense.
Category:Definitions/Topology
Category:Definitions/Topological Bases
\end{definition}