Definition:Basic Open Set

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Let $T = \left({S, \tau}\right)$ be a topological space.

Let $\mathcal B \subseteq \tau$ be a basis for $T$.

Let $U \in \mathcal B$.

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.