The Stacks project

Example 5.8.12. Let $Z$ be an infinite set and let $z\in Z$. We furnish $Z$ with the topology whose closed sets are $Z$ and the finite subsets of $Z\setminus \{ z\} $. Then $Z$ is sober but its subspace $Z\setminus \{ z\} $ is not quasi-sober.

Comments (2)

Comment #3545 by Laurent Moret-Bailly on

Just a suggestion on the "set difference" notation: the \smallsetminus command produces , which I think is better that (the latter is indistinguishable from a quotient by a left action).

Comment #3677 by on

OK, I never knew about this command... but it turns out it isn't in the latex packages we use in the Stacks project... I've been traditionally hesitant to load more packages than absolutely needed... If more people second your suggestion then I'll make the change globally.

There are also:

  • 8 comment(s) on Section 5.8: Irreducible components

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View Example 5.8.12 as pdf