Stone--Weierstrass Approximation Revisited

TL;DR

This paper extends the classical Stone--Weierstrass theorem to functions valued in lattice normed spaces using Boolean valued transfer, broadening the scope of approximation theory.

Contribution

It introduces a novel approach to approximation in lattice normed spaces by employing Boolean valued transfer techniques.

Findings

Extended Stone--Weierstrass theorem to lattice normed spaces

Developed Boolean valued transfer methodology for approximation

Broadened the applicability of approximation theory to ordered spaces

Abstract

The aim of the present article is to extend the Stone--Weierstrass theorem to functions ranging in a lattice normed space and order rather than topological approximation. We proceed with the machinery of Boolean valued transfer from lattice normed space to normed space.