Orientation of manifolds - definition*
... Hn (M, M − K; Z), such that for each x ∈ K the map induced by the inclusion maps [M ]K to a generator of Hn (M, M − x; Z) and the classes mapped to each other under the maps induced by the inclusion Hn (M, M − K; Z) → Hn (M, M − K 0 ; Z) for all K 0 ⊂ K. The images of the classes [M ]K in Hn (M, M − ...
... Hn (M, M − K; Z), such that for each x ∈ K the map induced by the inclusion maps [M ]K to a generator of Hn (M, M − x; Z) and the classes mapped to each other under the maps induced by the inclusion Hn (M, M − K; Z) → Hn (M, M − K 0 ; Z) for all K 0 ⊂ K. The images of the classes [M ]K in Hn (M, M − ...
![[edit] Construction of the Lebesgue measure](http://s1.studyres.com/store/data/001141507_1-534aa5aeea25b32a8226835f0ebc16e0-300x300.png)
18.03 Differential Equations, Lecture Note 33
... the columns of the matrix weighted by the entries in the column vector. When is this product zero? One way is for x = 0 = y. If [a ; c] and [b ; d] point in different directions, this is the ONLY way. But if they lie along a single line, we can find x and y so that the sum cancels. Write A = [a b ; ...
... the columns of the matrix weighted by the entries in the column vector. When is this product zero? One way is for x = 0 = y. If [a ; c] and [b ; d] point in different directions, this is the ONLY way. But if they lie along a single line, we can find x and y so that the sum cancels. Write A = [a b ; ...
