Bourbaki

Exercise 14, § 8

General Topology, IV, p. 64

Now prove that every closed subset of R is countable or has the power of the continuum (use Exercise 12 b) of IV, p. 63 and Exercise 17 of I, p. 107).

Solution

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