The Non-Existence of Algorithm Deciding Whether a Constructive Compact Topological Space is Simply Connected
DOI:
https://doi.org/10.61173/v524km74Keywords:
constructive mathematics, topology, funda-mental group, algorithmAbstract
This paper discusses the non-existence of an algorithm Q always deciding whether a constructive compact topological space is simply connected or not, that is whether its fundamental group is trivial or not. We construct a program R that generates compact topological spaces, then we use R and Q to get an extension of an unextendible function to get the contradiction and finish the proof.
References
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