The Stacks project

Definition 5.8.1. Let $X$ be a topological space.

  1. We say $X$ is irreducible, if $X$ is not empty, and whenever $X = Z_1 \cup Z_2$ with $Z_ i$ closed, we have $X = Z_1$ or $X = Z_2$.

  2. We say $Z \subset X$ is an irreducible component of $X$ if $Z$ is a maximal irreducible subset of $X$.

Comments (1)

Comment #8722 by Roy Shtoyerman on

It might be lacking a definition of an irreducible subset . I assume it's just irreducible as a space w.r.t. the subset topology, but it might be useful to elaborate for clarity.

There are also:

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

Post a comment

Your email address will not be published. Required fields are marked.

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.




In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 004V. Beware of the difference between the letter 'O' and the digit '0'.



View Definition 5.8.1 as pdf