Definition 2.11

Definition 2.11: As in the metric setting, it is possible for a subset of $$X$$ to be neither open nor closed (e.g., in Example 2.2, $$\{a,b\}$$). It is also possible for a subset of $$X$$ to be both open and closed, which we call clopen. (E.g., if $$X$$ has the discrete topology, then every subset of $$X$$ is clopen).