Definition:Basis (Topology)/Specification of Topology

Definition

As a way of specifying a particular topology on a set, we can say:

Let $\tau$ be the topology which has the sets ... as a basis.

In such a case, those sets should all satisfy the axioms for a synthetic basis $(\text B 1)$ and $(\text B 2)$.

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.2$: Bases: Application $3.2.6$