Gμ-covers, strongly compact cardinals and factorization of maps from products in Unif and Top

Abstrakt

It is shown that numbers of coordinates of factorized (uniformly) continuous maps on limits of inverse systems in special subclasses of Unif or Top are bounded from above by mu-strongly compact cardinals and those bounds cannot be decreased. For instance, if there is no omega(1)-strongly compact (or uncountable measurable) cardinal, then for every cardinal kappa there exists a (uniformly) continuous map from a limit of an inverse system into a countable space that cannot be factorized via a limit of a subsystem of cardinality less than kappa.(c) 2023 Elsevier B.V.

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Klíčová slova

• Factoring maps
• Limits of inverse systems
• mu-strongly compact cardinal
• G(delta)-cover