The Stacks project

Definition 5.9.1. A topological space is called Noetherian if the descending chain condition holds for closed subsets of $X$. A topological space is called locally Noetherian if every point has a neighbourhood which is Noetherian.

Comments (1)

Comment #10143 by Edward van de Meent on

I don't think that "descending chain condition" is defined anywhere in the project. a quick search suggests that this is the first place it is mentioned in the stacks project. similar for ascending chain condition. Is this something that should be defined in the project?

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  • 8 comment(s) on Section 5.9: Noetherian topological spaces

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View Definition 5.9.1 as pdf