Extensions of Uniformly Continuous Pseudometrics

Extensions of totally bounded pseudometrics

Perturbed Smooth Lipschitz Extensions of Uniformly Continuous Functions on Banach Spaces

We show that if Y is a separable subspace of a Banach space X such that both X and the quotient X/Y have Cp-smooth Lipschitz bump functions, and U is a bounded open subset of X, then, for every uniformly continuous function f : Y ∩U → R and every ε > 0, there exists a Cp-smooth Lipschitz function F : X → R such that |F (y)− f(y)| ≤ ε for every y ∈ Y ∩U . If we are given a separable subspace Y o...

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...

Title: Continuous extensions

Continuous Extensions to Nystr

In this work, we consider interpolants for Nystrr om methods, i.e., second order initial value problems. We give a short introduction to the theory behind the discrete methods, and extend some of the work to continuous, explicit Nystrr om methods. Interpolants for continuous, explicit Runge-Kutta methods have been intensively studied by several authors, but there has not been much eeort devoted...