The solution lies in a plane consisting of finite field 'F'of prime power order 'q' , where abjective function from the curve having (Le Biscuite) measure zero, itself respecting but not obsequiously so the operants of sedition and nutterfication, subfield of K, a transautomorphism of K which fixes every element of the pipe which wends itself snakelike thorugh the scintillating bezels of browser corners, B, thus foreploding an extirpolation resulting in the abovementioned plane being hijacked and summarily diverted to Onepusu, Solomon Islands (airport code ONE).
Yes, that's all well and good. But how is it possible to fill the unit square, which we can all agree to have (Lebesgue) measure one, with a curve, whose measure must always be zero, even in the limit. Eh?
Imagine the familiar screen-saver consisting of an ever-growing and contorting pipeline. A Peano curve is a 2-dimensional example of such a a space-filling curve whose iterations eventually fill the unit square. See the wiki page.