Finite Subset of Metric Space is Closed
Jump to navigation
Jump to search
Theorem
Let $M = \struct {A, d}$ be a metric space.
Let $S \subseteq A$ be finite.
Then $S$ is closed in $M$.
Proof
From Metric Space is Hausdorff, $M$ is Hausdorff.
From Finite Subspace of Hausdorff Space is Closed, $S$ is closed.
$\blacksquare$