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arXiv · 2006.00020

Locally Constant Constructive Functions and Connectedness of Intervals

Viktor Chernov
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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. 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 nonempy sets.

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Viktor Chernov. 2020-05-29. Locally Constant Constructive Functions and Connectedness of Intervals. https://doi.org/10.1093/logcom/exaa038

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