View source for Chain

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===In ordered sets===
The same as a [[totally ordered set]]: in a general [[partially ordered set]], a subset which is totally ordered with respect to the induced order.

===In algebraic topology===
A formal linear combination of simplices (of a triangulation, of a simplicial set and, in particular, of singular simplices of a topological space) or of cells. In the most general sense it is an element of the group of chains of an arbitrary (as a rule, free) chain complex. A chain with coefficients in a group $G$ is an element of the tensor product of a chain complex by the group $G$.

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  N.E. Steenrod,   S. Eilenberg,   "Foundations of algebraic topology" , Princeton Univ. Press  (1966)</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top">  P.J. Hilton,   S. Wylie,   "Homology theory. An introduction to algebraic topology" , Cambridge Univ. Press  (1960)</TD></TR></table>