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There is an exercise in the beginning of Bott and Tu's Diff. Forms in

Algebraic Topology, of finding the DeRham Cohomology of X=R^2-P-Q,

where P,Q are two different points in R^2. What is confusing is that,

at the point of the exercise, we have not yet introduced Mayer-Vietoris

sequence. And we cannot either use tricks like using the fact that X retracts

(i.e., is homotopic to) the figure-8 space, aka, wedge of two circles, and then

using algebraic topology.

Bottom line is all we seem to have available is just the definition of

DeRham cohomology as the quotient space of closed forms modded out by

exact forms.

Any Ideas.?

Thanks.