Goes to the advanced topics rather fast. Contains up-to-date proofs for free inverse semigroups, topics on biordered sets, Isbell's zigzags , and some combinatorics of transformation semigroups.] Fundamentals of semigroup theory, 1995. [Probably the best introduction. Contains more advanced material such as Isbell's zigzags , and the free inverse semi-groups]. G. Lallement, Semigroups and combi...

Given a group G of permutations of a finite n-element set Xn and a transformation f of Xn, the G-closure 〈f : G〉 of f is the semigroup generated by all the conjugates of f by permutations in G. A semigroup S of transformations of Xn is G-normal if GS = G, where GS consists of all the permutations h of Xn such that h−1fh ∈ S for all f ∈ S. We may assume that Xn is a chain and we let POIn be the ...

Definition 1.1. A topological semigroup is a topological space S together with a continuous function m : S × S → S such that S is Hausdorff andm is associative. A subsemigroup of a semigroup S is a nonvoid set A ⊂ S such that A2 ⊂ A, and A is called a subgroup of S if it is a group with respect tom. An element e of a topological semigroup S is called an idempotent if e2 e. Similarly, an element...

We have shown recently that, given a metric space X, the coarse equivalence classes of metrics on two copies X form an inverse semigroup M(X). Here we give description set E(M(X)) idempotents this and its Stone dual Xˆ. also construct ?-additive measures Xˆ from finitely additive probability that vanish bounded subsets.

In this paper, we study the word problem of automaton semigroups and automaton groups from a complexity point of view. As an intermediate concept between automaton semigroups and automaton groups, we introduce automaton-inverse semigroups, which are generated by partial, yet invertible automata. We show that there is an automaton-inverse semigroup and, thus, an automaton semigroup with a PSpace...