Note on pointwise periodic semigroups

A Note on Pointwise Dimensions

This short note describes a connection between algorithmic dimensions of individual points and classical pointwise dimensions of measures.

A Note on Extending Semicharacters on Semigroups

The purpose of this note is to give a necessary and sufficient condition for a semicharacter on a subsemigroup of a commutative semigroup G to be extendable to a semicharacter on G. A bounded complex function x on a semigroup G is called a semicharacter of G if x(x)9^0 for some xEG and x(xy) = x(%)x(y) ior all x, yEG. Semicharacters were introduced by Hewitt and Zuckerman [l] and in a slightly ...

A note on infinitely distributive inverse semigroups

By an infinitely distributive inverse semigroup will be meant an inverse semigroup S such that for every subset X ⊆ S and every s ∈ S, if ∨ X exists then so does ∨ (sX), and furthermore ∨ (sX) = s ∨ X. One important aspect is that the infinite distributivity of E(S) implies that of S; that is, if the multiplication of E(S) distributes over all the joins that exist in E(S) then S is infinitely d...

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,...

A Note on Amalgams of Inverse Semigroups