Question

If X and Y are CW complex's, define the attaching maps for the

CW complex X x Y, and the characteristic maps.

Answer 1

The attaching maps for the CW complex X x Y attach cells in the product space to cells in X and Y. The characteristic maps determine the topology of X x Y.

Step-by-step explanation:

The attaching maps for the CW complex X x Y are the maps that attach cells in the product space to cells in X and Y. More specifically, if X has an n-cell and Y has an m-cell, then the attaching map for the product X x Y attaches the (n+m)-cell of X x Y to the product of the attaching maps of X and Y.

The characteristic maps for the CW complex X x Y are the maps that determine the topology of X x Y. The characteristic map for the product X x Y is the composition of the characteristic maps of X and Y.