It's often interesting to try and endow a collection of spaces with the same structure as the individual objects in the

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It S Often Interesting To Try And Endow A Collection Of Spaces With The Same Structure As The Individual Objects In The 1 (81.12 KiB) Viewed 53 times

It's often interesting to try and endow a collection of spaces with the same structure as the individual objects in the collection. For us: can we turn the collection of all subspaces of a vector space into a vector space itself? Let V (V) denote the collection of all vector subspaces of V, and define U + W as the sum of subspaces U, W EU(V) (defined as in class). Question: Are there any abelian group axioms (i.e. commutativity, associativity, identity, and inverses) that are not satisfied by this operation?