Separately nowhere constant functions; n-cube and \alpha-prism densities


Krzysztof Ciesielski and Andrés Millán

J. Appl. Anal. 11(1) (2005), 49-62.

A function f from a countable product X of of Polish spaces Xi into a Polish space is separately nowhere constant provided it is nowhere constant on every section of X. We show that every continuous separately nowhere constant function is one-to-one on a product of perfect subsets of Xi's. This result is used to distinguish between n-cube density notions for different n\leq\omega, where \omega-cube density is a basic notion behind the Covering Property Axiom CPA formulated by Ciesielski and Pawlikowski. We will also distinguish, for different values of \alpha<\omega1, between the notions of \alpha-prism densities --- the more refined density notions used also in CPA.

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Last modified September 12, 2005.