Suppose $X_1$ and $X_2$ are isometric and $X_1$ is a complete space; show that $X_2$ is a complete space. Here I need somebody to help me or to give me ideas.
To show $X_2$ is complete space
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0Use the definition of a complete space, show that because $X_2$ is isometric to $X_1$ every Cauchy sequence in $X_2$ can be pulled to a Cauchy sequence in $X_1$, and therefore it must have a limit. – 2012-04-14