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.


Then the empty set $\O$ is closed in $M$.