# topologically complemented subspace

Let $$X$$ be a Banach space and let $$M$$ be a topologically complemented subspace of $$X$$.

If a closed subspace $$N \subset X$$ is isomorphic to $$M$$, is it topologically complemented too?

• No. See this. – David Mitra Mar 21 at 9:24
• Thank you David. – AyoubGhx Mar 21 at 16:44