Abundance of $E$-order-preserving transformation semigroups
Lei Sun, Xuefeng Han · TURKISH JOURNAL OF MATHEMATICS · 2015
Let T X be the full transformation semigroup on anite totally ordered set X = f 1 < 2 < ::: < ng ( n � 3) and E be a nontrivial equivalence relation on X. In this paper, we consider a subsemigroup of T X dened by EOPX = f f 2 T X : 8 x;y 2 X; ( x;y) 2 E;xy ) ( f ( x) ;f ( y)) 2 E;f ( x) � f ( y) g and present a necessary and sufficient condition under which the semigroup EOPX is abundant.