Let $F$ be a field and $\kappa$ be an infinite cardinal. Assume (by AC) that $F^X$ has a base, i.e. there exists a cardinal $\lambda$ so that $$ F^\kappa := \prod_{i \in \kappa} F \cong \bigoplus_{i \in \lambda} F =: F^{(\lambda)} .$$ I know that $\lambda$ is uniquely determined. Is there a general formula to derive $\lambda$ from $\kappa$?
2026-03-26 09:45:42.1774518342
Algebraic Dimension of function space
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