Boundary (Topology)/Examples/Integers in Real Numbers

Examples of Boundaries in the context of Topology

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

Let $\Z$ be the set of integers.


Then the boundary of $\Z$ in $\struct {\R, \tau_d}$ is $\Z$ itself.


Sources

  • 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: Exercise $3.9: 31$
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