Closure (Topology)/Examples/Union of Singleton with Open Interval

Example of Closure in the context of Topology

Let $\R$ be the set of real numbers.

Let $H \subseteq \R$ be the subset of $\R$ defined as:

$H = \set 0 \cup \openint 1 2$

Then the closure of $H$ in $\R$ is:

$H^- = \set 0 \cup \closedint 1 2$

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $3$: Continuity generalized: topological spaces: $3.7$: Definitions: Examples $3.7.13$