Michael

Canada

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Meaning of the identity $\det(A+B)+\text{tr}(AB) = \det(A)+\det(B) + \text{tr}(A)\text{tr}(B)$ (in dimension $2$)

linear-algebra reference-request determinant quadratic-forms trace asked May 5 '15 at 6:22

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32 votes

Why is the inclusion of the tensor product of the duals into the dual of the tensor product not an isomorphism?

vector-spaces asked Apr 5 '11 at 23:46

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29 votes

Are there uncountably many non homeomorphic ways to topologize a countably infinite set?

set-theory general-topology asked Apr 24 '11 at 8:48

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28 votes

Why the whole exterior algebra?

linear-algebra abstract-algebra vector-spaces category-theory multilinear-algebra asked Mar 10 '15 at 20:06

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23 votes

Is a closed set with the "unique nearest point" property convex?

geometry hilbert-spaces asked Jan 9 '13 at 22:53

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20 votes

Are the coordinate functions of a Hamel basis for an infinite dimensional Banach space discontinuous?

functional-analysis banach-spaces asked Apr 16 '11 at 9:03

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17 votes

Who has the upper hand in a generalized game of Risk?

probability recreational-mathematics closed-form asked Nov 26 '11 at 1:12

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17 votes

Is a countable, totally disconnected Hausdorff space necessarily totally separated? How about zero-dimensional?

general-topology asked Nov 20 '11 at 0:29

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17 votes

If two Borel measures coincide on all open sets, are they equal?

general-topology measure-theory asked Jul 21 '14 at 21:19

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16 votes

CSB inquality: is $\|x\|^2\|y\|^2 - \langle x,y \rangle^2$ a square in any obvious way?

linear-algebra abstract-algebra inequality asked Mar 25 '13 at 18:10

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Michael

Meaning of the identity $\det(A+B)+\text{tr}(AB) = \det(A)+\det(B) + \text{tr}(A)\text{tr}(B)$ (in dimension $2$)

Why is the inclusion of the tensor product of the duals into the dual of the tensor product not an isomorphism?

Are there uncountably many non homeomorphic ways to topologize a countably infinite set?

Why the whole exterior algebra?

Is a closed set with the "unique nearest point" property convex?

Are the coordinate functions of a Hamel basis for an infinite dimensional Banach space discontinuous?

Who has the upper hand in a generalized game of Risk?

Is a countable, totally disconnected Hausdorff space necessarily totally separated? How about zero-dimensional?

If two Borel measures coincide on all open sets, are they equal?

CSB inquality: is $\|x\|^2\|y\|^2 - \langle x,y \rangle^2$ a square in any obvious way?