We consider weighted algebras of holomorphic functions on a Banach space. We determine conditions on a family of weights that assure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study the spectra of weighted algebras and endow them with an analytic structure. We also deal with composition operators and algebra homomorphisms, in particular to ...

This paper denes and investigates the ergodic proper-ties of the entropy of a countable partition of a fuzzy dynamical sys-tem at different points of the state space. It ultimately introducesthe local fuzzy entropy of a fuzzy dynamical system and proves itto be an isomorphism invariant.

Akbarov’s theory of holomorphic reflexivity for topological Hopf algebras has been developed in two directions, namely, by the complication definitions when expanding scope and their simplification restricting. In framework latter approach, we establish associated with locally finite countable groups second-countable profinite groups. Abelian case, is described terms close to classical ones.

We present some applications of Popa’s Superrigidity Theorem to the theory of countable Borel equivalence relations. In particular, we show that the universal countable Borel equivalence relation E∞ is not essentially free.

We show that the automorphism group of the countable universal distributive lattice has strong uncountable cofinality, and we adapt the method to deduce the strong uncountable cofinality of the automorphism group of the countable universal generalized boolean algebra.

Examples of spaces X are constructed for which Cp(X) is not normal but all closed discrete subsets are countable. A monolithic example is constructed in ZFC and a separable first countable example is constructed using ♦.

We force a first countable, normal, locally compact, initially ω1-compact but non-compact space X of size ω2. The onepoint compactification of X is a non-first countable compactum without any (non-trivial) converging ω1-sequence.

In this paper we examine the structure of countable closed invariant sets under a dynamical system on a compact metric space. We are motivated by a desire to understand the possible structures of inhomogeneities in one-dimensional non-hyperbolic sets (inverse limits of finite graphs) particularly when those inhomogeneities form a countable set. All of the previous literature regarding the colle...

In the early days of the development of model theory it was considered natural and was certainly beneficial to assume that the theories under investigation were in a countable language. The primary advantage of this assumption was the presence of the Omitting Types Theorem of Grzegorczyk, Mostowski, and Ryll-Nardzewski [1], which generalized arguments of Henkin [3] and Orey [8]. Following this,...

We exhibit some uncountable groups with Property (FH). In particular, these groups do not have Kazhdan’s Property (T), which is known to be equivalent to Property (FH) for countable groups. Our first examples rely on a theorem of Delzant, which states that every countable group embeds in a group with Property (T). We give two constructions. The first is a (non-explicit) transfinite induction on...