topological embedding

Let $X$ , $Y$ be topological spaces. A map $f:X\\to Y$ is said to be an embedding (or imbedding) if the restriction $f:X\\to f[X]$ is homeomorphism.

The notation $f:X\\hookrightarrow Y$ is often used for embeddings.

The embeddings correspond to the subspaces. Observe that $f$ and the inclusion map of the subspace $f[X]$ into $X$ differ only up to a homeomorphism.

References

1 Wikipedia’s entry on http://en.wikipedia.org/wiki/embeddingEmbedding
2 S. Willard, General topology, Addison-Wesley, Massachussets, 1970.

单词	TopologicalEmbedding
释义	topological embedding Let $X$ , $Y$ be topological spaces. A map $f:X\\to Y$ is said to be an embedding (or imbedding) if the restriction $f:X\\to f[X]$ is homeomorphism. The notation $f:X\\hookrightarrow Y$ is often used for embeddings. The embeddings correspond to the subspaces. Observe that $f$ and the inclusion map of the subspace $f[X]$ into $X$ differ only up to a homeomorphism. References 1 Wikipedia’s entry on http://en.wikipedia.org/wiki/embeddingEmbedding 2 S. Willard, General topology, Addison-Wesley, Massachussets, 1970.
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