Definition:Net (Metric Space)/Finite Net

Definition

Let $M$ be a metric space.

Let $\epsilon \in \R_{>0}$ be a strictly positive real number.

A finite $\epsilon$-net for $M$ is an $\epsilon$-net for $M$ which is a finite set.

Sources

• 1975: W.A. Sutherland: Introduction to Metric and Topological Spaces ... (previous) ... (next): $7.2$: Sequential compactness
• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $5$: Metric Spaces: Complete Metric Spaces