N-skeleton

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This article is not about the topological skeleton concept of computer graphics

In mathematics, particularly in algebraic topology, the n-skeleton of a topological space X presented as a simplicial complex, or CW complex, refers to the subspace X_n that is the union of the simplices of X (resp. cells of X) of dimensions m ≤ n.

These subspaces increase with n. The 0-skeleton is a discrete space, and the 1-skeleton a topological graph. The skeletons of a space are used in obstruction theory, to construct spectral sequences by means of filtrations, and generally to make inductive arguments. They are particularly important when X has infinite dimension, in the sense that the X_n do not become constant as n → ∞.