Continuous embedding: Difference between revisions

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==Definition==
 
Let ''X'' and ''Y'' be two normed vector spaces, with norms ||&middot;||<sub>''X''</sub> and ||&middot;||<sub>''Y''</sub> respectively, such that <math>''X \subseteq ''&nbsp;&sube;&nbsp;''Y</math>''. If the [[identity function|inclusion map (identity function)]]
 
:<math>i : X \hookrightarrow Y : x \mapsto x</math>