I have seen some references to Banach's homogeneous space problem from 1932 which was solved by Gowers.
Could I ask what this problem actually states, I have tried searching and cannot find anything (or nothing which was free access anyway).
2026-03-30 01:47:03.1774835223
What is Banach's Homogeneous Space Problem of 1932?
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For me, the very first Google hit for "Banach homogeneous space problem" is https://arxiv.org/abs/math/9205207, which is open access. It clearly states the question and describes the progress up to 1992:
(In context, here "$X$ and $Y$ are isomorphic" means "there is a bijective linear homeomorphism between them".)
Gowers' proof appears to be in the following paper:
It is also freely available on arXiv at https://arxiv.org/abs/math/0501105.