The reverse mathematics of the Tietze extension theorem
Paul Shafer · Proceedings of the American Mathematical Society · 2016
We prove that several versions of the Tietze extension theorem for functions with moduli of uniform continuity are equivalent to W K L 0 \mathsf {WKL}_0 over R C A 0 \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).