3 ms·
Because continuity is not required here. There are non-continuous bijections between R and R^2.
by Skeime 3y ago
Because continuity is not required here. There are non-continuous bijections between R and R^2.
- yarg 3y agoHow is continuity not required? If there are holes in the map does it really cover the whole space?
- Skeime 3y agoI think you have misconceptions about what continuity means and I’m not even sure what you mean with holes. As a simpler example: The map that multiplies each rational number by -1 and keeps irrational numbers as they are is bijective (it’s its own inverse), however it is nowhere continuous.