Boundary (Topology)/Examples/Half-Open Real Interval

Examples of Boundaries in the context of Topology

Let $\struct {\R, \tau_d}$ be the real number line with the usual (Euclidean) topology.

Let $\hointl a b$ be a half-open interval of $\R$.

Then the boundary of $\hointl a b$ is the set of its endpoints $\set {a, b}$.

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.7$: Definitions: Definition $3.7.32$