Bourbaki

Exercise 8, § 1

Commutative Algebra, VIII, p. 82

Let X be a topological space. Now prove that the mapping x \mapsto \dim_x(X) of X into \overline{\mathbf{R}} is upper semi-continuous.

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.