A Variation on the Stone-Weierstrass Theorem
نویسندگان
چکیده
منابع مشابه
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...
متن کاملStrengthened 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...
متن کاملOn a Generalization of the Stone-Weierstrass Theorem
A categorical version of the famous theorem of Stone and Weierstrass is formulated and studied in detail. Several applications and examples are given.
متن کاملA Stone-weierstrass Type Theorem for Semiuniform Convergence Spaces
A Stone-Weierstraß type theorem for semiuniform convergence spaces is proved. It implies the classical Stone-Weierstraß theorem as well as a Stone-Weierstraß type theorem for filter spaces due to Bentley, Hušek and Lowen-Colebunders [1].
متن کاملA Stone-weierstrass Theorem without Closure under Suprema
For a compact metric space X , consider a linear subspace A of C{X) containing the constant functions. One version of the Stone-Weierstrass Theorem states that, if A separates points, then the closure of A under both minima and maxima is dense in C{X). By the Hahn-Banach Theorem, if A separates probability measures, A is dense in C{X). It is shown that if A separates points from probability mea...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1963
ISSN: 0002-9939
DOI: 10.2307/2034972