Topological embedding
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Link in with subspace topology, important for disjoint union topology
Contents
Definition
An injective and continuous map that is a homeomorphism onto its image (considering that image as imbued with the subspace topology) is called a topological embedding[1] (or just an embedding if the context makes this obvious)[1]
Results
- The canonical injection for a topological subspace is a topological embedding
- A continuous injective map that is either an open map or a closed map is a topological embedding
- There are topological embeddings that are neither closed or open.
- A surjective topological embedding is a homeomorphism
TODO: Example of embedding that is neither a closed map or an open map
References
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