The Stacks project

Definition 5.10.5. Let $X$ be a topological space. We say that $X$ is equidimensional if every irreducible component of $X$ has the same dimension.

Comments (2)

Comment #7817 by Jinyong An on

For the definition of equidimensional topological space, it allows that each irreducible components has same dimension of infinity? Or, finiteness of each (same) dimension of the irreducible components is required?

Comment #8045 by on

With the definitions as given an equidimesional space can have dimension and (in the latter case it is empty).

There are also:

  • 3 comment(s) on Section 5.10: Krull dimension

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Your email address will not be published.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 0058. Beware of the difference between the letter 'O' and the digit '0'.