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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

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View Definition 5.10.5 as pdf