Quasi-equicontinuous sets of functions

A Note on Extreme Sets for Quasi-Continuous Functions

It is known that for Ω a connected separable metric space, a function Ω → R which at every point attains a weak local extremummust have countable image. Let Ω ⊂ R be a bounded domain and f : Ω → C a measurable, bounded, quasi-continuous function. For n ∈ Z+, we show that if |f | has countable image then f attains weak local extremum at each point of a dense open subset. We show by examples the ...

Equicontinuous Delone Dynamical Systems

We characterize equicontinuous Delone dynamical systems as those coming from Delone sets with strongly almost periodic Dirac combs. Within the class of systems with finite local complexity the only equicontinuous systems are then shown to be the crystalline ones. On the other hand, within the class without finite local complexity, we exhibit examples of equicontinuous minimal Delone dynamical s...

From Well-Quasi-Ordered Sets to Better-Quasi-Ordered Sets

We consider conditions which force a well-quasi-ordered poset (wqo) to be betterquasi-ordered (bqo). In particular we obtain that if a poset P is wqo and the set Sω(P ) of strictly increasing sequences of elements of P is bqo under domination, then P is bqo. As a consequence, we get the same conclusion if Sω(P ) is replaced by J (P ), the collection of non-principal ideals of P , or by AM(P ), ...

On Pre-θ-Open Sets and Two Classes of Functions

Quasi-orthogonal expansions for functions in BMO

For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M