= Isomorphic embedding
{title2=$c\|x\|\leq\|Tx\|$}
An isomorphic embedding of <normed vector spaces> is an <injective> <bounded linear operator> whose inverse on its <image> is bounded. Equivalently $\|Tx\|\geq c\|x\|$ for some $c>0$. The two-sided bounds make the domain and its <image> carry equivalent <norms>. If the domain is a <Banach space>, a convergent sequence $Tx_n$ has a <Cauchy sequence> of preimages, so its limit remains in the <image>; thus the <image> is closed.
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