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

Authors

Krzysztof Ciesielski, West Virginia UniversityFollow

Document Type

Article

Publication Date

2005

College/Unit

Eberly College of Arts and Sciences

Department/Program/Center

Mathematics

Abstract

A function f from a countable product X of of Polish spaces X_i 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 X_i'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.

Digital Commons Citation

Ciesielski, Krzysztof, "Separately nowhere constant functions; n-cube and \alpha-prism densities" (2005). Faculty & Staff Scholarship. 842.
https://researchrepository.wvu.edu/faculty_publications/842