Definition:Compact Space/Real Analysis

Definition
Let $\R$ be the real number line considered as a topological space under the Euclidean topology.

Let $H \subseteq \R$.

Also see

 * Equivalence of Definitions of Compact Subset of Real Numbers


 * Heine-Borel Theorem, where it is proved that this definition is equivalent to the topological definition when $\R$ is considered with the Euclidean topology.