Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances

Generating transformation semigroups using endomorphisms of preorders, graphs, and tolerances

Let ΩΩ be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of ΩΩ, then we write U ≈ V if there exists a finite subset F of ΩΩ such that the subgroup generated by U and F equals that generated by V and F . The relative rank of U in ΩΩ is the least cardinality of a subset A of ΩΩ such that the union of U and A generates ΩΩ. We study the notions of relative...

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...

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...

UNIVERSAL COMPACTIFICATIONS OF TRANSFORMATION SEMIGROUPS

We extend the notion of semigroup compactification to the class of transformation semigroups, and determine the compactifications which are universal with respect to some topological properties.

Endomorphisms and synchronization, 2: Graphs and transformation monoids