The separable quotient problem asks whether every infinite-dimensional Banach space has an infinite-dimensional separable Banach quotient space. Equivalently, it asks for a bounded linear surjection onto an infinite-dimensional separable Banach space. A separable subspace alone does not supply such a quotient. The real and complex formulations can be considered separately.
Separable Quotient Problem
See also
Banach Quotient Space, Banach Space, Continuum Hypothesis, Measurable Cardinal, Real-Valued Measurable Cardinal, Separable Space, Zermelo-Fraenkel Set TheoryExplore with Wolfram|Alpha
References
Ferrando, J. C.; Kakol, J.; López-Pellicer, M.; and Sliwa, W. "On the Separable Quotient Problem for Banach Spaces." Funct. Approx. Comment. Math. 59, 153-173, 2018. https://doi.org/10.7169/facm/1704.Cite this as:
Weisstein, Eric W. "Separable Quotient Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/SeparableQuotientProblem.html