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MathNet 1985 — Part 01 Question 21

Math Olympiad Vault · MathNet 1985 — Part 01

Question 21

be $\mathcal{P}$ the set of the points of the plane and $f: \mathcal{P} \rightarrow \mathcal{P}$ An application that meets the following three conditions:

a) $f$ It is bijective.

b) for each line $r$ from the plane, $f(r)$ It's a straight.

c) for each line $r$, the straight $f(r)$ Is it parallel or coincident with $r$. What possible transformations can be $f$?