Category:Nowhere Dense iff Complement of Closure is Everywhere Dense
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This category contains pages concerning Nowhere Dense iff Complement of Closure is Everywhere Dense:
Let $T = \struct {S, \tau}$ be a topological space.
Let $H \subseteq S$.
Then $H$ is nowhere dense in $T$ if and only if $S \setminus H^-$ is everywhere dense in $T$, where $H^-$ denotes the closure of $H$.
Corollary
Let $H$ be a closed set of $T$.
Then $H$ is nowhere dense in $T$ if and only if $S \setminus H$ is everywhere dense in $T$.
Pages in category "Nowhere Dense iff Complement of Closure is Everywhere Dense"
The following 3 pages are in this category, out of 3 total.