Composition of axial functions of products of finite sets

Krzysztof P/lotka¹

¹ Department of Mathematics University of Scranton Scranton, PA 18510, U.S.A.

Colloquium Mathematicum, Tome 107 (2007) no. 1, pp. 15-20.

Résumé

We show that every function $f: A \times B \to A \times B$, where $|A|\le 3$ and $|B| \omega $, can be represented as a composition $f_1 \circ f_2 \circ f_3 \circ f_4 $ of four axial functions, where $f_1$ 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 $f: A \times B \to A \times B$ such that $f\not =f_1 \circ f_2 \circ f_3 \circ f_4$ for any axial functions $f_1, f_2, f_3, f_4$, whenever $f_1$ is a horizontal function.

Détail

DOI : 10.4064/cm107-1-3

Keywords: every function times times where omega represented composition circ circ circ axial functions where vertical function prove every finite set cardinality least there exist finite set function times times circ circ circ axial functions whenever horizontal function