Definition:Embedded Submanifold

Definition

Let $M$ be a smooth manifold with or without boundary.

Let $S \subseteq M$ be a subset.

Suppose $S$ is a topological manifold in the subspace topology.

Suppose $S$ is endowed with the smooth differentiable structure such that the inclusion map $i_S : S \to M$ is a smooth embedding.

Then $S$ is called the embedded submanifold of $M$.

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Sources

• 2013: John M. Lee: Introduction to Smooth Manifolds (2nd ed.): $\S 5$: Submanifolds. Embedded Submanifolds