Definition:Bounded Subset of Connected Riemannian Manifold

Definition
Let $\struct {M, g}$ be a connected Riemannian manifold.

Let $A \subseteq M$ be a subset.

Let $p,q \in M$ be points.

Let $d_g$ be the Riemannian distance.

Let $C \in \R$ be a constant.

Suppose:


 * $\exists C \in \R : \forall p, q \in A : \map {d_g} {p, q} \le C$

Then $A$ is said to be bounded.