Definition:Nowhere Dense/Definition 2

Definition

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

Let $H \subseteq S$.

$H$ is nowhere dense in $T$ if and only if:

$H^-$ contains no open set of $T$ which is non-empty

where $H^-$ denotes the closure of $H$.

Also see

• Equivalence of Definitions of Nowhere Dense

Sources

• 1978: Lynn Arthur Steen and J. Arthur Seebach, Jr.: Counterexamples in Topology (2nd ed.) ... (previous) ... (next): Part $\text I$: Basic Definitions: Section $1$: General Introduction: Countability Properties