N-skeleton


N-skeleton

:"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 (resp. 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". In other words, given an inductive definition of a complex, the "n"-skeleton is obtained by stopping at the "n"-th step.

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" → ∞.

In geometry

In geometry, a "k"-skeleton of "n"-polytope P (functionally represented as skel"k"("P")) consists of all "i"-polytope elements of dimension up to "k". [Peter McMullen, Egon Schulte, Abstract Regular Polytopes, Cambridge University Press, 2002. ISBN 0-521-81496-0 (Page 29)]

References

External links

* [http://mathworld.wolfram.com/Skeleton.html Mathworld: Skeleton]


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