Definition:Everywhere Dense/Metric Space

Definition

Let $M = \struct {A, d}$ be a metric space.

Let $B \subseteq A$ be a subset of $A$.

Then $B$ is (everywhere) dense in $M$ if and only if every point of $A$ is a limit point of a sequence of points of $B$.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): dense set
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dense set