Continuous linear extension of functions

On Simultaneous Extension of Continuous Partial Functions

For a metric space X let Cvc(X) (that is, the set of all graphs of real-valued continuous functions with a compact domain in X) be equipped with the Hausdorff metric induced by the hyperspace of nonempty closed subsets of X×R. It is shown that there exists a continuous mapping Φ : Cvc(X) → Cb(X) satisfying the following conditions: (i) Φ(f)| dom f = f for all partial functions f. (ii) For every...

Extension of Continuous Functions in /3n

Fitting piecewise linear continuous functions

We consider the problem of fitting a continuous piecewise linear function to a finite set of data points, modeled as a mathematical program with convex objective. We review some fitting problems that can be modeled as convex programs, and then introduce mixed-binary generalizations that allow variability in the regions defining the best-fit function’s domain. We also study the additional constr...

Aggregate Functions, Conservative Extension, and Linear Orders

1 Summary Practical database query languages are usually equipped with some aggregate functions. For example, \\nd mean of column" can be expressed in SQL. However, the manner in which aggregate functions were introduced in these query languages leaves something to be desired. Breazu-Tannen, Buneman, and Wong 3] introduced a nested relational language NRC(=) based on monads 16, 24] and structur...

Normed Linear Spaces of Continuous Functions

1. Introduction. In addition to its well known role in analysis, based on measure theory and integration, the study of the Banach space B(X) of real bounded continuous functions on a topological space X seems to be motivated by two major objectives. The first of these is the general question as to relations between the topological properties of X and the properties (algebraic, topological, metr...