Some density results for uniformly continuous functions

On uniformly continuous functions for some profinite topologies

Given a variety of finite monoids V, a subset of a monoid is a V-subset if its syntactic monoid belongs to V. A function between two monoids is V-preserving if it preservesV-subsets under preimages and it is hereditary V-preserving if it is W-preserving for every subvariety W of V. The aim of this paper is to study hereditary V-preserving functions when V is one of the following varieties of fi...

Rings of Uniformly Continuous Functions

There is a natural bijective correspondence between the compactifications of a Tychonoff space X, the totally bounded uniformities on X, and the unital C∗-subalgebras of C∗(X) (the algebra of bounded continuous complex valued functions on X) with what we call the completely regular separation property. The correspondence of compactifications with totally bounded uniformities is well know and ca...

Some results on continuous frames for Hilbert Spaces

Between continuous and uniformly continuous functions on R n ∗

We study classes of continuous functions on R that can be approximated in various degree by uniformly continuous ones (uniformly approachable functions). It was proved in [BDP1] that no polynomial function can distinguish between them. We construct examples that distinguish these classes (answering a question from [BDP1]) and we offer appropriate forms of uniform approachability that enable us ...

Some Results on Convex Spectral Functions: I

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...