SEPARATELY NOWHERE CONSTANT FUNCTIONS; n-CUBE AND α-PRISM DENSITIES
نویسنده
چکیده
A function f from a countable product X = ∏ i 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 α < ω1, between the notions of α-prism densities — the more refined density notions used also in CPA.
منابع مشابه
Applications of the Covering Property Axiom
Applications of the Covering Property Axiom Andrés Millán Millán The purpose of this work is two-fold. First, we present some consequences of the Covering Property Axiom CPA of Ciesielski and Pawlikowski which captures the combinatorial core of the Sacks’ model of the set theory. Second, we discuss the assumptions in the formulation of different versions of CPA. As our first application of CPA ...
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