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).
