How could you recognize a halting oracle if you saw one?
How could you recognize an infinite string of "1"s if you saw one? You can't, because there could always be a 0 later.
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I can give you an algorithm that describes that sequence.
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I can point to physical machines and say that these compute the same thing as this Turing machine up to a certain size input
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and that if you keep expanding its memory, it will only diverge from the TM for physical reasons, not formal ones
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I can think of a TM that uses a halting oracle as an interactive program that asks the user whether TMs halt
End of conversation
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In Cantor space, singleton sets are not open, and hence cannot be effectively open.
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