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 (2)

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:

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

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View Definition 5.8.1 as pdf