Let
f be a
one-to-one correspondence of the points in a
plane.
Prove or disprove the following statement:
"If f maps circles to circles, then it maps straight lines to straight lines."
(In reply to
re: Proof by JLo)
You bring up a valid point. But I'm not sure that this is easily fixed. Upon further thought, the line might be mapped to the union of C(0) and any number of other C(x).
Such a mapping would require some pretty big discontinuities in the mapping, so I still don't think a counterexample exists. But it will be difficult to prove it so.
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Posted by Tristan
on 2006-11-17 15:34:33 |
re(2): Proof
