Definition:Everywhere Dense/Definition 3

Definition

Let $T = \struct {S, \tau}$ be a topological space.

Let $H \subseteq S$ be a subset.

The subset $H$ is (everywhere) dense in $T$ if and only if every neighborhood of every point of $S$ contains at least one point of $H$.

Also see

• Equivalence of Definitions of Everywhere Dense

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