Document Type


Publication Date



Eberly College of Arts and Sciences




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.

Included in

Mathematics Commons



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.