Sectional switching mapping in semilattices
Ivan Chajda, Petr Emanovský · Miskolc mathematical notes/Mathematical notes · 2006
Consider a _-lattice S D .S; _/ with a greatest element 1.An interval Œa; 1 for a 2 S is called a section.A mapping f of Œa; 1 onto itself is called a switching mapping if f .a/D 1, f .1/D a and for x 2 Œa; 1, a 6 D x 6 D 1 we have a 6 D f .x/6 D 1.We study _-lattices with switching mappings on all the sections.If for p; q 2 S , p Ä q the mapping on the section Œq; 1 is determined by that of Œp; 1, we say that the compatibility condition is satisfied.We will get conditions for antitony of switching mappings and a connection with complementation in sections will be shown.