- #1
Happiness
- 690
- 31
Consider the following map ##f## that maps an annulus to a larger annulus: ##f: (r, \theta)\to(r+1, \theta)##. ##f## maps the annulus in the region ##1\leq r\leq2## to the annulus in the region ##2\leq r\leq3##. Clearly, the area is not preserved.
Next, is the converse true? That is, must an area-preserving map be a bijective map? How about a length-preserving map and a volume-preserving map? Must they be bijective?
Next, is the converse true? That is, must an area-preserving map be a bijective map? How about a length-preserving map and a volume-preserving map? Must they be bijective?