Talk:Noetherian topological space

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This is the current revision of this page, as edited by Cewbot (talk | contribs) at 03:02, 9 March 2024 (Maintain {{WPBS}}: 1 WikiProject template. Remove 1 deprecated parameter: field.). The present address (URL) is a permanent link to this version.

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The section on compactness was removed because Noetherian spaces are not necessarily compact. Indeed, the affine line is Noetherian, but not compact. —Preceding unsigned comment added by 98.248.125.245 (talk) 21:13, 9 November 2009 (UTC)[reply]

Exercise II.2.13a) of Hartshorne shows that X is Noetherian iff every open subset is (quasi)-compact. In view of this, I will revert your edit for now. If you are discussing a stronger notion of Noetherian, can you please provide a reference? Thanks. RobHar (talk) 21:51, 9 November 2009 (UTC)[reply]
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