Enumerating compact spaces
Serikzhan Badaev, Nikolay Bazhenov, Birzhan Kalmurzayev, Alexander Melnikov, Manat Mustafa
Source abstract
We investigate the existence of a 1 1 - 1 1 effective (a.k.a. Friedberg) enumeration in the class of compact Polish spaces. We first prove a number of negative results. We show that there is no Friedberg enumeration of computably compact spaces up to isometry, homeomorphism, computable isometry, or computable homeomorphism. The main result of the article is that there exists a Friedberg enumeration of all primitive recursively compact spaces up to isometry.
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