Algebraic Topology, Part 1: General Notions

Stuff

Some stuff.

Consider open sets U1,U2X. In general f(Ui) may not be open, however for an open map f,

f(U1U2)=f(U1)f(U2) is open.

The Van Kampen theorem: If U1 and U2 are open sets, U1U2=X, and U1U2=X is simply connected, then:

π1(U1,x0)π1(U2,x0)π1(X,x0).