Tight representations of semilattices and inverse semigroups

Tight Representations of Semilattices and Inverse Semigroups

By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse semigroup S in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of Booleannes present in the semilattice of idempotents of ...

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...

Geometri Representations of Inverse Semigroups

A Note on Representations of Inverse Semigroups

It is known [l; 2] that every inverse semigroup 5 has a faithful representation as a semigroup of (1, l)-mappings of subsets of a set A into A. The set A may be taken as the set of elements of 5 and the (1, l)-mappings as mappings of principal left ideals of 5 onto principal left ideals of 5. If £ is the set of idempotents of 5 then there is also a representation of 5, not necessarily faithful,...

Weightable quasi-metric semigroups and semilattices

In [Sch00] a bijection has been established, for the case of semilattices, between invariant partial metrics and semivaluations. Semivaluations are a natural generalization of valuations on lattices to the context of semilattices and arise in many different contexts in Quantitative Domain Theory ([Sch00]). Examples of well known spaces which are semivaluation spaces are the Baire quasi-metric s...