Simplicial Map

Let  and  be simplicial complexes, and let  be a map. Suppose that whenever the vertices , ...,  of  span a simplex of , the points , ...,  are vertices of a simplex of . Then  can be extended to a continuous map  such that

implies

The map  is then called the linear simplicial map induced by the vertex map  (Munkres 1993, p. 12).

REFERENCES:

Hatcher, A. Algebraic Topology. Cambridge, England: Cambridge University Press, 2002.

Munkres, J. R. Elements of Algebraic Topology. New York: Perseus Books Pub., 1993.