It is proved that if A is aregular uniform algebra on a compact Hausdorff space X in which every closed ideal is an M-ideal, then A = C(X).

The chapter represents a comparison of ultrapower fields (loosely surreals, hyper-reals, long line) and number fields generated by infinite primes having a physical interpretation in Topological Geometrodynamics. Ultrapower fields are discussed in very physicist friendly manner in the articles of Elemer Rosinger and these articles are taken as a convenient starting point. The physical interpret...

It is shown that if E is a Frechet space with the strong dual E∗ then Hb(E ∗), the space of holomorphic functions on E∗ which are bounded on every bounded set in E∗, has the property (DN) when E ∈ (DN) and that Hb(E∗) ∈ (Ω) when E ∈ (Ω) and either E∗ has an absolute basis or E is a Hilbert-Frechet-Montel space. Moreover the complementness of ideals J(V ) consisting of holomorphic functions on E...

In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space (Y, d). We show that this binary operator is commutative, non-associative, idempotent, invariant to multiplication by a constant weight and possesses an identity element. We also cover the properties of the weighted cumulative Frechet mean. These tools allow us ...

We introduce the Hopf algebra of uniform block permutations and show that it is self-dual, free, and cofree. These results are closely related to the fact that uniform block permutations form a factorizable inverse monoid. This Hopf algebra contains the Hopf algebra of permutations of Malvenuto and Reutenauer and the Hopf algebra of symmetric functions in non-commuting variables of Gebhard, Ros...