Composition of axial functions of products of finite sets

• Autorzy: Krzysztof Płotka
• Języki publikacji: EN

Abstrakty

EN

We show that every function f: A × B → A × B, where |A| ≤ 3 and |B| < ω, can be represented as a composition f₁ ∘ f₂ ∘ f₃ ∘ f₄ of four axial functions, where f₁ is a vertical function. We also prove that for every finite set A of cardinality at least 3, there exist a finite set B and a function f: A × B → A × B such that f ≠ f₁ ∘ f₂ ∘ f₃ ∘ f₄ for any axial functions f₁, f₂, f₃, f₄, whenever f₁ is a horizontal function.

Kategorie tematyczne

• 08A02: Relational systems, laws of composition
• 03E20: Other classical set theory (including functions, relations, and set algebra)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2007
• Tom: 107
• Numer: 1
• Strony: 15-20

Daty

wydano

2007

Twórcy

autor

Krzysztof Płotka

• Department of Mathematics, University of Scranton, Scranton, PA 18510, U.S.A.

Identyfikatory

DOI

10.4064/cm107-1-3