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Is there a collectionwise normal topological vector space which is not paracompact?

Let M2 denote the set of all matrices of 2 X 2. Determine if M2 is a vector space when considered with the?

  • Let M2 denote the set of all matrices of 2 X 2. Determine if M2 is a vector space when considered with the standard addition of vectors, but with scalar multiplication given by α ⋆(a b c d) = (αa b c αd) . In case M2 fails to be a vector space with these definitions, list at least one axiom that fails to hold. Justify your answer.

  • Answer:

    (a+b)u = au + bu does not hold true :)

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(a+b)u = au + bu does not hold true :)

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