一句话：引入 Z-稳定性概念，研究其点态与一致版本，并给出构造性过渡所需条件与递归反例。
论文在 Bishop 构造性数学框架下引入 Z-稳定性，用以刻画函数 f 将度量空间映入赋范空间时，若 ||f(x)|| 很小则 x 接近 f 的零点这一直觉。作者先研究点态 Z-稳定性及相关的“良好行为”概念，随后给出递归反例，说明经典论证不能从点态 Z-稳定性推出紧度量空间上的一致版本。为实现构造性过渡，论文引入 positivity principle（等价于可分离杠的 Brouwer 扇定理）和 limited anti-Specker property（序列紧性的直觉主义对应物）。最后探讨 limited anti-Specker property、positivity 性质与 Brouwer 扇定理之间的联系。
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.
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@article{BridgesDM16,
title = {Z-stability in Constructive Analysis},
author = {Douglas Bridges and James Dent and Maarten McKubre-Jordens},
journal = {Logical Methods in Computer Science},
volume = {Volume 12, Issue 3},
year = {2017},
doi = {10.2168/lmcs-12(3:10)2016}
}