Definition 5.11.1. Let X be a topological space. Let Y \subset X be an irreducible closed subset. The codimension of Y in X is the supremum of the lengths e of chains
Y = Y_0 \subset Y_1 \subset \ldots \subset Y_ e \subset X
of irreducible closed subsets in X starting with Y. We will denote this \text{codim}(Y, X).
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