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Section: Highlights of the Year

Highlights of the Year

We worked on the computable aspects of an elementary problem in real analysis: extending a continuous function on a larger domain. More precisely, if a real-valued function $f$ is defined on an interval $[0,a)$ (with $0<a<1$) and is computable there, under which conditions can it be extended to a computable function on $[0,1]$? Our results show how the answer depends on $a$ and on the way $f$ converges at $a$. This provides new characterizations of already existing classes of real numbers previously defined in computability theory. Our work was presented at LICS 2017 [19].