Bourbaki

Exercise 7, § 9

General Topology, I, p. 106

Give an example of a projective system (X_α, f_{αβ}) of quasi-compact spaces whose projective limit is empty (remark that in the space of Example 2 of I, p. 60, every subspace is quasi-compact).

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.