Beth definability and the Stone-Weierstrass Theorem

The Stone-weierstrass Theorem

The really new thing about Stone’s approach to the approximation theorem was the approach via lattices of continuous functions, although Lebesgue had noticed the importance of approximating the absolute-value function earlier. There is a segment of the mathematical community formed of people who are as likely to encounter a lattice in their work as an algebra and for whom the lattice version of...

Strengthened Stone-weierstrass Type Theorem

The aim of the paper is to prove that if L is a linear subspace of the space C(K) of all real-valued continuous functions defined on a nonempty compact Hausdorff space K such that min(|f |, 1) ∈ L whenever f ∈ L, then for any nonzero g ∈ L̄ (where L̄ denotes the uniform closure of L in C(K)) and for any sequence (bn)n=1 of positive numbers satisfying the relation P∞ n=1 bn = ‖g‖ there exists a se...

An Institution-independent Proof of the Beth Definability Theorem

Beth Definability in Institutions

BETH DEFINABILITY IN INSTITUTIONS MARIUS PETRIA∗ AND RĂZVAN DIACONESCU Abstract. This paper studies definability within the theory of institutions, a version of abstract model This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definab...

Spaces of Rational Maps and the Stone-weierstrass Theorem

It is shown that Segal’s theorem on the spaces of rational maps from CP to CPn can be extended to the spaces of continuous rational maps from CPm to CPn for any m 6 n. The tools are the Stone-Weierstraß theorem and Vassiliev’s machinery of simplicial resolutions.