Inclusion Mapping is Embedding

Theorem

Let $T = \struct{S, \tau}$ be a topological space.

Let $T_H = \struct{H, \tau_H}$ be a topological subspace of $T$, where $H \subseteq S$.

Let $i_H : H \to S$ be the inclusion mapping of $H$ into $S$.


Then $i_H$ is a embedding of $T_H$ into $T$.

Proof


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Sources

  • 2011: John M. Lee: Introduction to Topological Manifolds (2nd ed.) ... (previous) ... (next): $\S 3$: New Spaces From Old: Subspaces. Topological Embeddings
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