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    $\begingroup$ Could you summarise how these three papers answer the question? $\endgroup$ Commented Sep 12, 2024 at 1:24
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    $\begingroup$ The fact that Top is a co-quasivariety is already mentioned by the OP, though. Does anything in these papers actually address the questions that were asked? $\endgroup$ Commented Sep 14, 2024 at 5:41
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    $\begingroup$ @KevinCarlson thanks for this comment, it is true that my answer does not provide any true additional insight. I'll leave it just as an expansion of the question. $\endgroup$ Commented Sep 15, 2024 at 9:13