Bourbaki

Exercise 15, § 8

General Topology, IV, p. 64

Now prove that the set of open sets in R and the set of compact, perfect and totally disconnected sets in R have the power of the continuum.

Solution

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Machine translation of the English, by gpt-5-6-mini. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.