Continuous embedding: Difference between revisions

Revision as of 18:49, 10 October 2007

Revision as of 15:23, 15 December 2007

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==Examples==

* A finite-dimensional example of a continuous embedding is given by a natural embedding of the [[real line]] ''X'' = '''R''' into the plane ''Y'' = '''R'''²², where both spaces are given the Euclidean norm:

::<math>i : \mathbf{R} \to \mathbf{R}^{2} : x \mapsto (x, 0)</math>