Let \(X\) and \(Y\) be normed vector spaces with \(X\subset Y\). If the inclusion map
\begin{equation*} i\colon X\hookrightarrow Y\colon x \mapsto x, \end{equation*}is continuous, i.e. for some \(C>0\)
\begin{equation*} \lVert x\rVert_Y\le C\lVert x\rVert_X, \end{equation*}for every \(x\in X\), then \(X\) is said to be continuously embedded in \(Y\).
It is customary to write \(X\hookrightarrow Y\) if \(X\) is continuously embedded in \(Y\).