N-SKELETON

(Redirected from Skeleton (topology))

:''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'' → ∞.