I would suggest you look at more of Escardo's writing and research on related topics. https://www.cs.bham.ac.uk/~mhe/papers/omniscient-journal-revised.pdf https

I would suggest you look at more of Escardo's writing and research on related topics. https://www.cs.bham.ac.uk/~mhe/papers/omniscient-journal-revised.pdf https://www.cs.bham.ac.uk/~mhe/papers/omniscient-journal-rev... is one such paper. The issues of compactness of cantor space in classical and constructive math and the computational interpretation of principles like Brouwer's fan theorem in relation to dependent choice and weak König's lemma is really deep.