Algebraic Topology, Part 1: General Notions
Stuff
Some stuff.
Consider open sets U1,U2∈X. In general f(Ui) may not be open, however for an open map f,
f(U1∪U2)=f(U1)∪f(U2) is open.The Van Kampen theorem: If U1 and U2 are open sets, U1∪U2=X, and U1∩U2=X is simply connected, then:
π1(U1,x0)∗π1(U2,x0)≅π1(X,x0).