Abstract

We prove that every locally constant constructive function on an interval is in fact a constant function. This answers a question formulated by Andrej Bauer [ 1]. As a related result, we show that an interval consisting of constructive real numbers is in fact connected but can be decomposed into the disjoint union of two sequentially closed nonempty sets.

中文翻译：

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局部恒定的构造函数和区间的连通性

摘要

我们证明区间上的每个局部常数构造函数实际上都是常数函数。这回答了安德烈·鲍尔[1]提出的问题。作为一个相关的结果，我们表明一个由构造实数组成的区间实际上是相连的，但可以分解为两个顺序封闭的非空集的不相交并集。