Empty Set is Closed
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Theorem
Topological Space
Let $T = \struct {S, \tau}$ be a topological space.
Then $\O$ is closed in $T$.
Metric Space
Let $M = \struct {A, d}$ be a metric space.
Then the empty set $\O$ is closed in $M$.
Normed Vector Space
Let $M = \struct {X, \norm {\, \cdot \,} }$ be a normed vector space.