Topics in Uniform Approximation of Continuous Functions by Ileana Bucur & Gavriil Paltineanu

Author:Ileana Bucur & Gavriil Paltineanu
Language: eng
Format: epub
ISBN: 9783030484125
Publisher: Springer International Publishing

Proof

The proof results from Theorem 2.3.1 for . Indeed, the set is a closed subset of C(Z, [0, 1]) which separates the points of the compact set and contains the constant functions 0, 1 and at least a constant function 0 < c < 1. From Theorem 4.18 in [2], it follows that . □

Corollary 2.3.4

Let X be a Hausdorff locally compact space, and let be a closed convex cone containing the constant functions 0, 1 and having the property that for any u, v ∈ βX, π(u)≠π(u) there is some φ ∈ C(X, [0, 1]) such that and (βφ)(u)≠(βφ)(v). We suppose also that for any x ∈ X there exists a compact subset K x ⊂ X such that

Then, there exists a finite number of equivalence classes and an equal number of functions with the properties:

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.