Metric Space is Open and Closed in Itself

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Theorem

Let $M = \struct {A, d}$ be a metric space.

Then $A$ is both open and closed in $M$.


Proof

From Metric Space is Open in Itself, $A$ is open in $M$.

From Metric Space is Closed in Itself, $A$ is closed in $M$.

$\blacksquare$


Sources