Locally Constant Constructive Functions and Connectedness of Intervals

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.

arXiv comment4 pages, 0 figures. Minor corrections and improvements. References updated

Cited by in corpus (1)

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