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topological embedding
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(Definition)
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Let $X$ , $Y$ be topological spaces. A map $\Map fXY$ is said to be an embedding (or imbedding) if the restriction $\Map fX{\Img fX}$ is homeomorphism.
The notation $\Emb fXY$ is often used for embeddings.
The embeddings correspond to the subspaces. Observe that $f$ and the inclusion map of the subspace $\Img fX$ into $X$ differ only up to a homeomorphism.
- 1
- Wikipedia's entry on Embedding
- 2
- S. Willard, General topology, Addison-Wesley, Massachussets, 1970.
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"topological embedding" is owned by kompik. [ full author list (4) ]
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Cross-references: inclusion map, subspaces, homeomorphism, restriction, embedding, map, topological spaces
There are 6 references to this entry.
This is version 5 of topological embedding, born on 2005-09-24, modified 2007-04-16.
Object id is 7385, canonical name is Embedding4.
Accessed 3796 times total.
Classification:
| AMS MSC: | 54C25 (General topology :: Maps and general types of spaces defined by maps :: Embedding) | | | 52B05 (Convex and discrete geometry :: Polytopes and polyhedra :: Combinatorial properties ) |
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Pending Errata and Addenda
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