# On the completeness of topologically isomorphic spaces

Let $$(E_1, tau_1)$$ to be a locally convex space and let $$(E_2, tau_2)$$ to be a complete space locally convex. Assume that $$T: (E_1, tau_1) longrightarrow (E_2, tau_2)$$ is a topological isomorphism (i.e. $$T$$ is linear, bijective, continuous and its inverse $$T ^ {- 1}$$ is continuous too).

Is it true that space $$(E_1, tau_1)$$ is necessarily complete?

Thank you for all the advice / comments.