GENERATING SETS OF STRICTLY ORDER-PRESERVING TRANSFORMATION SEMIGROUPS ON A FINITE SET

The Ranks of Some Transformation Semigroups on a Finite Set

Generating Sets of Order Preserving Mappings

Sierpiński proved in 1935 that any countable set of mappings on an infinite set X is contained in a subsemigroup of the semigroup of all maps on X, where this subsemigroup is generated by just two mappings. Since then, it has been of interest whether the result also holds when certain restrictions are placed on the properties of the maps. In this paper we investigate the minimum number of order...

Generating Uncountable Transformation Semigroups

We consider naturally occurring, uncountable transformation semigroups S and investigate the following three questions. (i) Is every countable subset F of S also a subset of a finitely generated subsemigroup of S? If so, what is the least number n such that for every countable subset F of S there exist n elements of S that generate a subsemigroup of S containing F as a subset. (ii) Given a subs...

compactifications and representations of transformation semigroups

this thesis deals essentially (but not from all aspects) with the extension of the notion of semigroup compactification and the construction of a general theory of semitopological nonaffine (affine) transformation semigroup compactifications. it determines those compactification which are universal with respect to some algebric or topological properties. as an application of the theory, it is i...

Divisors of Semigroups of Order-Preserving mappings on a Finite Chain

Let a finite semilattice S be a chain under its natural order. We show that if a semigroup T divides a semigroup of full order preserving transformations of a finite chain, then so does any semidirect product S o T .