| For shapes constructed from other shapes, typically the dimensions of the pieces are related to the dimensions of the whole. The constructions we consider are the union, intersection, and product. Typical dimension rules are these. | |
| How is the dimension of the product of A and B related to the dimensions A and B? Typically, the dimension of the product is the sum of the dimensions. | |
| How is the dimension of the union of A and B related to the dimensions A and B? Typically, the dimension of the union is the maximum of the dimensions. | |
| How is the dimension of the intersection of A and B related to the dimensions A and B? Typically, the dimension of the intersection is the sum of the dimensions, minus the dimension of the space in which A and B live. | |
| Here are some Exercises. | |