Generalizations of the Stone-Weierstrass approximation 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...
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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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A categorical version of the famous theorem of Stone and Weierstrass is formulated and studied in detail. Several applications and examples are given.
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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.
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In its basic form, the approximation theorem referred to provides simple n n combinatorial models for spaces ~ E X, where X is a connected based space. The first such result was given by James [26], who showed that ~EX is equivalent to the James construction MX. The unpublished preprint form of Dyer and gashof's paper [25] gave an approximation to QX = lira ~nEnx, and Milgram [41] gave a cellul...
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ژورنال
عنوان ژورنال: Proceedings of the Japan Academy, Series A, Mathematical Sciences
سال: 1968
ISSN: 0386-2194
DOI: 10.3792/pja/1195520986