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1 Journal of Applied Analysis

1 2005

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Separately nowhere constant functions; n-cube and α-prism densities

Ciesielski K., Millán A.

Journal of Applied Analysis

2005

Vol. 11, nr 1

49-62

A function f from a countable product X= Πi Xi of Polish spaces 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 ≤ ω, where ω-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 ∝ < ω 1, between the notions of a-prism densities -the more refined density notions used also in CPA.