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Iris Loeb, Indecomposability of ℝ and ℝ \ {0} in Constructive Reverse Mathematics, Logic Journal of the IGPL, Volume 16, Issue 3, June 2008, Pages 269–273, https://doi.org/10.1093/jigpal/jzn006
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Abstract
It is shown that—over Bishop's constructive mathematics—the indecomposability of ℝ is equivalent to the statement that all functions from a complete metric space into a metric space are sequentially nondiscontinuous. Furthermore we prove that the indecomposability of ℝ \ {0} is equivalent to the negation of the disjunctive version of Markov's Principle. These results contribute to the programme of Constructive Reverse Mathematics.
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