Abstrakt
Results in this paper concern finding a cardinal number Kappa, as small as possible, such that every uniformly or proximally continuous mapping from a given subspace X of a product IL Xi into some A factorizes via a subspace of Pi J Xi with |J| <= Kappa. In some cases we substantially improve Vidossich theorem from [12].
Influenced by investigating locally co-presentable categories in [8], also cardinals Kappa are found such that the above factorization hold for all products HI Xi from an epireflective subclass C of Unif2, their closed subspaces X and spaces A generating C. That situation is close to factorizing maps on limits of inverse systems via limits of smaller inverse subsystems.
We define and investigate a new cardinal function on uniform spaces helping to find a convenient factorization. (c) 2021 Elsevier B.V. All rights reserved.