Definition:Diameter (Metric Space)

Definition

Let $M = \left({A, d}\right)$ be a metric space.

Let $\varnothing \subset S \subseteq M$ be bounded in $M$.

Then the diameter of $S$ is defined as:

$\operatorname {diam} \left({S}\right) := \sup \left\{{d \left({x, y}\right): x, y \in S}\right\}$.

From this, the diameter can be intuitively understood as the greatest possible distance between two points in $S$.

Sources

• Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (1970)... (previous)... (next): $\text{I}: \ \S 5$: Complete Metric Spaces
• W.A. Sutherland: Introduction to Metric and Topological Spaces (1975): Definition $2.2.13$