文章基本信息

标题：Z-stability in constructive analysis
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作者：Douglas Bridges ; James Dent ; Maarten McKubre-Jordens 等
期刊名称：Logical Methods in Computer Science
印刷版ISSN：1860-5974
电子版ISSN：1860-5974
出版年度：2016
卷号：12
期号：3
页码：1
DOI：10.2168/LMCS-12(3:10)2016
出版社：Technical University of Braunschweig
摘要：We introduce Z-stability, a notion capturing the intuition that if a function f maps a metric space into a normed space and if the norm of f(x) is small, then x is close to a zero of f. Working in Bishop's constructive setting, we first study pointwise versions of Z-stability and the related notion of good behaviour for functions. We then present a recursive counterexample to the classical argument for passing from pointwise Z-stability to a uniform version on compact metric spaces. In order to effect this passage constructively, we bring into play the positivity principle, equivalent to Brouwer's fan theorem for detachable bars, and the limited anti-Specker property, an intuitionistic counterpart to sequential compactness. The final section deals with connections between the limited anti-Specker property, positivity properties, and (potentially) Brouwer's fan theorem for detachable bars.
其他关键词：Constructive; Z-stability; well behaved; anti-Specker; positivity principle.