Optimal subcategories and Stone-Weierstrass
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...
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The two main results in this paper are analogues of the Stone-Weierstrass theorem for real-valued functions, obtained by using different function space topologies. The first (Theorem 2.3) is a Stone-Weierstrass theorem for unbounded functions. The second (Theorem 3.6) is a theorem for bounded functions ; it is stronger than the usual theorem because the topology is larger than the uniform topol...
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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...
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The compact Hausdorff space X has the CSWP iff every subalgebra of C(X,C) which separates points and contains the constant functions is dense in C(X,C). Results of W. Rudin (1956), and Hoffman and Singer (1960), show that all scattered X have the CSWP and many non-scattered X fail the CSWP, but it was left open whether having the CSWP is just equivalent to being scattered. Here, we prove some g...
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We give a general version of Bryc’s theorem valid on any topological space and with any algebra A of real-valued continuous functions separating the points, or any wellseparating class. In absence of exponential tightness, and when the underlying space is locally compact regular and A constituted by functions vanishing at infinity, we give a sufficient condition on the functional Λ(·)|A to get ...
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ژورنال
عنوان ژورنال: Topology and its Applications
سال: 1987
ISSN: 0166-8641
DOI: 10.1016/0166-8641(87)90104-0