English

Locally Constant Constructive Functions and Connectedness of Intervals

Logic 2020-07-24 v2

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.

Keywords

Cite

@article{arxiv.2006.00020,
  title  = {Locally Constant Constructive Functions and Connectedness of Intervals},
  author = {Viktor Chernov},
  journal= {arXiv preprint arXiv:2006.00020},
  year   = {2020}
}

Comments

4 pages, 0 figures. Minor corrections and improvements. References updated

R2 v1 2026-06-23T15:55:04.395Z