HOMEWORK 5 – 2019
Exercise 1. Prove that the space which arises by glueing the Moebius band to the
boundary of a hole in the shere is the projektive plane.
Exercise 2. Prove that the plane X is not homeomorhic with the union Y of two
planes which have a line as an intersection. Hint: Compute homology groups of pairs
(X, X − {p}) and (Y, Y − {q}), where p ∈ X and q ∈ Y are points. Use excision
theorem.
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