“Stone-Weierstrass Theorem”的概念、定义、习题解题方法及翻译-数学辞典

单词

Stone-Weierstrass Theorem

释义

Stone-Weierstrass Theorem

Weierstrass' Approximation Theorem shows any continuous real-valued function on a closed bounded interval can be arbitrarily and uniformly approximated by polynomials; that is, there is a sequence of polynomials which uniformly converges to the function.

The theorem was considerably generalized by Stone to the following: let X be a compact Hausdorff space and let C(X) denote the algebra of continuous real-valued functions on X with the uniform topology; then any subalgebra A of C(X) is dense in C(X) if for any distinct points x,y in X there exists f in A such that f(x) ≠ f(y).

随便看

数学辞典收录了4151条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。