Let $X$ be a normed space. I'd like to show that all closed hyperplanes in $X$ are isomorphic.

My attempt

Let $H$ and $W$ be closed hyperplanes. We know $\dim(X/H)=\dim(X/W)=1$, therefore $(X/H)$ and $(X/W)$ are isomorphic. How to conclude that W and H are isomorphic?


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