User Mike F

43 votes

3 answers

6k views

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

asked May 5, 2015 at 6:22

34 votes

1 answer

6k views

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

asked Apr 5, 2011 at 23:46

31 votes

3 answers

2k views

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

asked Apr 24, 2011 at 8:48

29 votes

4 answers

3k views

Why the whole exterior algebra?

asked Mar 10, 2015 at 20:06

25 votes

2 answers

4k views

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

asked Jan 9, 2013 at 22:53

21 votes

1 answer

2k views

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

asked Apr 16, 2011 at 9:03

18 votes

1 answer

2k views

bound on the cardinality of the continuum? I hope not

asked Feb 4, 2011 at 8:48

18 votes

3 answers

2k views

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

asked Nov 20, 2011 at 0:29

17 votes

2 answers

724 views

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

asked Nov 26, 2011 at 1:12

17 votes

2 answers

3k views

Uniform convergence of difference quotients to the derivative

asked Nov 15, 2012 at 1:43

17 votes

3 answers

5k views

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

asked Jul 21, 2014 at 21:19

16 votes

4 answers

399 views

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

asked Mar 25, 2013 at 18:10

13 votes

1 answer

2k views

Product of quotient map a quotient map when domain is compact Hausdorff?

asked Aug 2, 2012 at 23:48

13 votes

2 answers

566 views

Is every suborder of $\mathbb{R}$ homeomorphic to some subspace of $\mathbb{R}$?

asked Nov 22, 2011 at 10:55

13 votes

6 answers

6k views

How do I show that $\int_{-\infty}^\infty \frac{ \sin x \sin nx}{x^2} \ dx = \pi$?

asked Feb 7, 2012 at 7:02

13 votes

1 answer

4k views

Taylor's theorem in Banach spaces

asked Sep 10, 2011 at 3:43

13 votes

1 answer

1k views

Central extensions versus semidirect products

asked Aug 8, 2017 at 2:17

11 votes

4 answers

18k views

Linear combinations of sine and cosine

asked Mar 28, 2014 at 7:14

10 votes

2 answers

363 views

Looking for theorem of form: If [curvature hypotheses, etc] then every class in $\pi_1(M)$ is uniquely represented by a closed geodesic

asked Apr 21, 2017 at 15:41

10 votes

1 answer

665 views

Dot product with which polynomial gives evaluation at $x_0$?

asked Oct 16, 2015 at 15:18

10 votes

2 answers

919 views

Is there a countable, regular space with no isolated points which is not homeomorphic to the rationals?

asked Oct 12, 2011 at 21:58

10 votes

1 answer

1k views

When can a real Banach space be made into a complex Banach space?

asked Nov 11, 2011 at 1:47

10 votes

1 answer

461 views

In a C-algebra, put $a^a \sim aa^*$. Transitivity fails?

asked Feb 23, 2013 at 21:02

9 votes

4 answers

2k views

one-dimensional inverse square laws

asked Feb 19, 2014 at 6:59

9 votes

1 answer

175 views

If a subset of the plane has open intersection with every line, is it open?

asked Oct 19, 2011 at 3:11

9 votes

1 answer

1k views

What is the ''right" norm for the Banach space tensor product in this situation?

asked Mar 8, 2011 at 5:08

9 votes

0 answers

112 views

Does $L^2(M)$ always admit a basis of nowhere-vanishing functions?

asked Oct 22, 2016 at 5:11

9 votes

2 answers

538 views

Cousin of the Vandermonde binomial identity

asked Mar 10, 2014 at 2:28

9 votes

4 answers

2k views

Degree of minimum polynomial at most $n$ without Cayley-Hamilton?

asked Apr 29, 2015 at 21:50

8 votes

3 answers

363 views

If there is already enough room to add all projections, does passing to matrices change anything?

asked May 12, 2014 at 21:39

Stack Exchange Network

161 Questions

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?

bound on the cardinality of the continuum? I hope not

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

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

Uniform convergence of difference quotients to the derivative

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?

Product of quotient map a quotient map when domain is compact Hausdorff?

Is every suborder of $\mathbb{R}$ homeomorphic to some subspace of $\mathbb{R}$?

How do I show that $\int_{-\infty}^\infty \frac{ \sin x \sin nx}{x^2} \ dx = \pi$?

Taylor's theorem in Banach spaces

Central extensions versus semidirect products

Linear combinations of sine and cosine

Looking for theorem of form: If [curvature hypotheses, etc] then every class in $\pi_1(M)$ is uniquely represented by a closed geodesic

Dot product with which polynomial gives evaluation at $x_0$?

Is there a countable, regular space with no isolated points which is not homeomorphic to the rationals?

When can a real Banach space be made into a complex Banach space?

In a C-algebra, put $a^a \sim aa^*$. Transitivity fails?

one-dimensional inverse square laws

If a subset of the plane has open intersection with every line, is it open?

What is the ''right" norm for the Banach space tensor product in this situation?

Does $L^2(M)$ always admit a basis of nowhere-vanishing functions?

Cousin of the Vandermonde binomial identity

Degree of minimum polynomial at most $n$ without Cayley-Hamilton?

If there is already enough room to add all projections, does passing to matrices change anything?