The Gap Between Partial and Full
Jorge Almeida, Mikhail Vladimirovich Volkov · International Journal of Algebra and Computation · 1998
We show that the interval of the lattice of semigroup pseudovarieties between the pseudovarieties generated by all semigroups of full and respectively, partial, order-preserving transformations of a finite chain, contains a chain isomorphic to the chain of real numbers (with the usual order). Similar results are proved for several related intervals.