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13 Dec 2009: Conclude thatπn1(SO(n)) is infinite for even n. 6. If V1 and V2 are two vector bundles over B, then V1 V2 is a bundle over B B. ... TheWhitney sum V1 V2 is defined to be (V1 V2), where : B B B is the diagonalmap.

23 Feb 2009: 1. Which of the following propositions are tautologies, that is, are true for all valuations?(a) (A B) (B A). ... b) A A.(c) (A B) (B A). (d) (A B) ((A B) A).

28 Jan 2009: α β γ = π A(). 4. A. A. B. B. ... A Bu. C. v. C. B. α. Corollary 2.8 Spherical Cosine Rule II.

26 Oct 2009: B}. Show thatif A and B are both closed and one of them is bounded then A B is closed. ... b) Is the space R[0, 1] of integrable functions on [0, 1], equipped with the uniform norm, complete?

18 Feb 2009: Show that σ(Q) = 0. (b) Suppose that M is a 4k-manifold which bounds a (4k 1)-manifold W. ... Showthat a diffeomorphism f : X X extends to X if and only if f([b]) = [b].

20 Feb 2009: Another line ncrosses at a (movable) point B and a fixed angle β. ... cos α =cosh b cosh c cosh acosh2 b 1. cosh2 c 1.

12 Feb 2009: Showthat a diffeomorphism f : X X extends to X if and only if f([b]) = [b]. ... If youlike, you may assume f is given by a linear map on R2.)This is false as stated; the condition should be f([b]) = [b].

29 Oct 2009: B}. Show thatif A and B are both closed and one of them is bounded then A B is closed. ... b) Is the space R[0, 1] of integrable functions on [0, 1], equipped with the uniform norm, complete?

20 Feb 2009: Another line ncrosses at a (movable) point B and a fixed angle β. ... cos α =cosh b cosh c cosh acosh2 b 1. cosh2 c 1.

22 Jan 2009: 5) Prove the statement (b) of problem (4) above by completing the following. ... 6) Let f : B B be a continuous map from the open disc B = {(x, y) R2 : x2 y2 < 1} into it-self.