Published online by Cambridge University Press: 09 February 2023
We present a systematic approach to the problem whether a topologically infinite-dimensional space can be made homogeneous in the Coifman–Weiss sense. The answer to the question is negative, as expected. Our leading representative of spaces with this property is $\mathbb {T}^\omega = \mathbb {T} \times \mathbb {T} \times \cdots $ with the natural product topology.
The author was supported by the Basque Government (BERC 2022-2025), by the Spanish State Research Agency (SEV-2017-0718) and by the Foundation for Polish Science (START 032.2022).