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

• Autorzy: Ciesielski K. , Millán A.
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

separately nowhere constant functions; cube density; prism density

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2005
• Tom: Vol. 11, nr 1
• Strony: 49--62
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Ciesielski K.

• Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA

autor

Millán A.

• Department of Mathematics, West Virginia University, Morgantown, WV 26506-6310, USA

Bibliografia

• [1] Ciesielski, K., Set Theory for the Working Mathematician, London Math. Soc. Stud. Texts 39, Cambridge Univ. Press, Cambridge, 1997.
• [2] Ciesielski, K., Pawlikowski, J., Covering Property Axiom CPAcube and its consequences, Fund. Math. 176(1) (2003), 63-75. (Preprint available.)
• [3] Ciesielski, K., Pawlikowski, J., Nice Hamel bases under the Covering Property Axiom, Acta Math. Hungar. 105(3) (2004), 197-213. (Preprint available.)
• [4] Ciesielski, K., Pawlikowski, J., Covering Property Axiom CPA. A Combinatorial Core of the Iterated Perfect Set Model, Cambridge Tracts in Math.164, Cambridge Univ. Press, Cambridge, 2004.
• [5] Kechris, A., Classical Descriptive Set Theory, Grad. Texts in Math. 156, Springer Verlag, New York, 1994.
• [6] Miller, A. W., Special subsets of the real line, in „Handbook of Set-Theoretic Topology” (K. Kunen and J.E. Vaughan, eds.), North-Holland, Amsterdam, 1984, 201-233.