Completeness of Normed spaces. I want to prove the following proposition
If $(X,||\cdot||)$ and $(X,||\cdot||')$ are homeomorphic, then $(X,||\cdot||)$ is complete if and only if $(X,||\cdot||')$ is complete.
So, I only know the definition of homeomorphic, and can't figure out how only with that I can prove that proposition. Can someone help me to prove this please?
Thanks a lot in advance :) 

Since $(X, ||\cdot || ) $ and $ (X, ||\cdot ||' )$ are homeomorphic the topologies generated by these norms are identical. Hence the identity map $\mbox{Id} :(X, ||\cdot || ) \to (X, ||\cdot ||' )$ is continiuous so the norms are equivalent. And from the equivalence of the norms it easily follows your assertion.
