Definition:Everywhere Dense/Definition 1

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Definition

Let $T = \left({S, \tau}\right)$ be a topological space.

Let $H \subseteq S$ be a subset.


The subset $H$ is (everywhere) dense in $T$ if and only if:

$H^- = S$

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


That is, if and only if every point in $S$ is a point or a limit point of $H$.


Also see


Sources