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- W4385699146 abstract "It is consistent with any possible value of the continuum c that every infinite-dimensional Banach space of density ? c condenses onto the Hilbert cube. Let ? < c be a cardinal of uncountable cofinality. It is consistent that the continuum be arbitrary large, no Banach space X of density ?, ? < ? < c, condenses onto a compact metric space, but any Banach space of density ? admits a condensation onto a compact metric space. In particular, for ? = ?1, it is consistent that c is arbitrarily large, no Banach space of density ?, ?1 < ? < c, condenses onto a compact metric space. These results imply a complete answer to the Problem 1 in the Scottish Book for Banach spaces: When does a Banach space X admit a bijective continuous mapping onto a comact metric space?" @default.
- W4385699146 created "2023-08-10" @default.
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- W4385699146 date "2023-01-01" @default.
- W4385699146 modified "2023-09-23" @default.
- W4385699146 title "Note on the Banach problem 1 of condensations of Banach spaces onto compacta" @default.
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- W4385699146 doi "https://doi.org/10.2298/fil2307183o" @default.
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