Products of Sets:
            If  and  are two non-empty sets, then Cartesian product  is defined as .
Projection Maps:
            Let A and B be non-empty sets, then it can be defined the following two functions
(1)  defined as  for all
(2)  defined as  for all

The above maps are called the projection maps on A and B respectively.

Note: Let  be non-empty sets, then the projection maps  can be defined similarly.

Product Topology:
            Let  be the product of topological spaces  and . The coarsest topology  on  with respect to which the projection maps  and  are continuous, is said to be product topology and thus the space  is said to be the product space.

Remarks:

• It may be observed that if  and  are distinct topological spaces then the collection  form a subbase for product topology on .
• It may be noted that if A and B are any open interval, then  will be open rectangle strips. Collection of open rectangle form a bases for usual topology on . So, generalizing this fact to the product of finite number of spaces  and  are topological spaces then  form a bases for product topology.