Usual Topology on:
            A collection of subsets of  which can be can be expressed as union of open intervals, forms a topology on , and is called topology on.

Remark:
            Every open interval is an open set but the converse may not be true.
                                      

Usual Topology on:
            Consider the Cartesian plane, then the collection of subsets of which can be expressed as union of open discs or open rectangles with edges parallel to coordinate axis from a topology, and is called usual topology on .

Usual Topology on:
            Consider the Cartesian plane, then the collection of subsets of which can be expressed as union of open spheres or open cubed with edges parallel to coordinate axis from a topology, and is called usual topology on .