You seem very sure for such a wild claim. The observable universe is finite, as for the whole universe, we have no idea (unless you know something that I don't).
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But we have at least measured the curvature of the observable universe and within experimental error the result is that it is flat. Which in turn would imply an infinite universe if this flatness is exact and general, i.e. not something exceptional in the observable universe.
There are manifolds that are flat and compact (i.e., not "infinite"). For example, flat tori.
Good point. How did I never realize that?