The reverse mathematics of the Tietze extension theorem

Shafer, Paul

doi:10.1090/proc/13217

The reverse mathematics of the Tietze extension theorem
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Proc. Amer. Math. Soc. 144 (2016), 5359-5370 Request permission

Abstract:

We prove that several versions of the Tietze extension theorem for functions with moduli of uniform continuity are equivalent to $\mathsf {WKL}_0$ over $\mathsf {RCA}_0$. This confirms a conjecture of Giusto and Simpson (2000) that was also phrased as a question in Montalbán’s Open questions in reverse mathematics (2011).

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