Posted:

**Oct 02, 2016 8:59 am**Everything in mathematics always depends on the definitions.

I think the natural way here would be like this. The "space" S would be the set of all points that are enclosed within a defined boundary: for instance the set of all points (x, y, z), where x, y and z have their usual Cartesian meanings, and x2 + y2 is no greater than 1 and z is at least zero and no more than 5. That would be a cylindrical space.

Similarly the "curve" C is the set of all points that are in the domain of a certain continuous function.

If every point that is an element of S is also an element of C, then clearly C "fills" S.

I think the natural way here would be like this. The "space" S would be the set of all points that are enclosed within a defined boundary: for instance the set of all points (x, y, z), where x, y and z have their usual Cartesian meanings, and x2 + y2 is no greater than 1 and z is at least zero and no more than 5. That would be a cylindrical space.

Similarly the "curve" C is the set of all points that are in the domain of a certain continuous function.

If every point that is an element of S is also an element of C, then clearly C "fills" S.