Geodesic
The bounding number $\mathfrak b$ and quotients in Banach spaces
Zbornik radova, Tome 22 (2025) no. 30, p. 73

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DOI

The problem whether every infinite dimensional Banach space has a separable infinite dimensional quotient is known as the separable quotient problem. In this survey, we review results connecting the bounding number $\mathfrak{b}$ to this problem and to the existence of uncountable biorthogonal systems in nonseparable Banach spaces. Our discussion highlights combinatorial methods that help differentiate the structure of Banach spaces of density equal to the bounding number $\mathfrak{b}$ from those with density smaller than $\mathfrak{b}$.
DOI : 10.64191/zr24040410102
Classification : 03–02 03E05, 46B26, 03E17, 46B20
Keywords: quotients, biorthogonal systems, bounding number 
Christina Brech. The bounding number $\mathfrak b$ and quotients in Banach spaces. Zbornik radova, Tome 22 (2025) no. 30, p. 73 . doi: 10.64191/zr24040410102
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     author = {Christina Brech},
     title = {The bounding number $\mathfrak b$ and quotients in {Banach} spaces},
     journal = {Zbornik radova},
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     doi = {10.64191/zr24040410102},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.64191/zr24040410102/}
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