Definition:Basic Open Set
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Definition
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.