Separable quotient problem for infinite-dimensional Banach spaces

Determine whether every infinite-dimensional Banach space has an infinite-dimensional separable quotient.

Background

The paper places its study of separable quotients of topological groups in the context of the classical Banach-space separable quotient problem. That problem asks whether every infinite-dimensional Banach space admits an infinite-dimensional separable quotient. The paper notes that, at the time of the cited account, the general problem remained unresolved, while the affirmative answer was known for important subclasses such as reflexive Banach spaces.

References

Its classical Banach-space form asks whether every infinite-dimensional Banach space has an infinite-dimensional separable quotient( see Problem~1.1 and the Scottish Book ). At the time of the account in , the general problem was open.

— Three Problems on Separable Quotients of Precompact Abelian Groups  (2609.26049 - Xie et al., 22 Sep 2026) in Section 1, Introduction