Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $X$ be a noetherian integral scheme. Let $Z\subset X$ be a set of closed points in $X$.

What is the dimension of the closure of $Z$?

share|cite|improve this question
In general $Z$ is not open in $\overline{Z}$ (think about schemes of finite type over a field). – user18119 Dec 10 '11 at 22:10
Ow I was confuse there. You're right. I could consider the set of closed points $Z$ in a curve. Its closure is the whole set. Moreover, $Z$ is not open in the curve, because the generic point is not closed. – Lucci Dec 11 '11 at 0:12
You mean the dimension of the closure compared to $\dim Z$ ? – user18119 Dec 12 '11 at 22:33

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.