Cellular Map

Let X and Y be CW-complexes and let X_n (respectively Y_n) denote the n-skeleton of X (respectively Y). Then a continuous map f:X->Y is said to be cellular if it takes n-skeletons to n-skeletons for all n=0,1,2,..., i.e, if

 f(X_n) subset= Y_n,

for all nonnegative integers n.

The contents of the cellular approximation theorem is that, in a certain sense, all maps between CW-complexes can be taken to be cellular.

See also

Cellular Approximation Theorem, CW-Complex

This entry contributed by Rasmus Hedegaard

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Hedegaard, Rasmus. "Cellular Map." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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