3
$\begingroup$

I have to learn for a very important test on monday but I don't get along with the following exercise from Bredon's book »Topology and Geometry«:

Let the projective plane $P^2=U_1\cup … \cup U_n$ where each $U_i$ is homeomorphic to the plane. Put $V_i=U_1\cup … \cup U_i$ for $1\leq i. Show that there is an $i\leq n$ such that $U_i\cap V_{i-1}$ is disconnected or empty.

Any hints or proofs?

Thank you very very much!

  • 0
    Your title has no relation to the actual question. It is of course true that there are empty sets in $P^2$ and there are also disconnected sets there...2011-11-26

0 Answers 0