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Apr
16
comment Are intersection of power set and power set of intersection equal?
@dave : in addition to the above, I strongly urge you to justify things like this to yourself. When you read something of the form "X if and only if Y", take it as a personal exercise; stop and try to prove that X implies Y and Y implies X. In this case, the implications follow directly from the definitions of what things mean.
Apr
15
answered Are intersection of power set and power set of intersection equal?
Apr
9
comment Root space of eigenvalues of a linear map
$\mathbb{C}^n$ is basically just finding the Jordan form of the operator. I guess my concern is that the basis for $\mathbb{C}^n$ that puts the matrix in Jordan form may not be vectors in $\mathbb{R}^n$, so I can't just directly use that decomposition?
Apr
7
revised Root space of eigenvalues of a linear map
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Apr
7
comment Root space of eigenvalues of a linear map
I abused notation slightly and was referring to all of the root spaces with the notation $E_\lambda$. I assumed it was obvious from context. I will edit accordingly.
Apr
7
asked Root space of eigenvalues of a linear map
Apr
1
awarded  Custodian
Mar
4
awarded  Tumbleweed
Mar
4
accepted Several questions concerning Alexander's Theorem
Mar
3
answered an open subspace of compact space
Mar
3
comment Several questions concerning Alexander's Theorem
math.cornell.edu/~hatcher/3M/3M.pdf specifically the proof begins on page 1 of this document
Mar
3
comment Several questions concerning Alexander's Theorem
Forgive me for being dense, but I really don't understand what you've written for question 2. I need to produce a map from the 3 ball to the region bounded by my topological disk. It looks like you're taking a point $(x,y,z)$ in the lower part of the 3 ball and mapping it onto a point $(x',y',z')$ in the region bounded by the topological disk so that $(x',y'z')$ has $(u,v)$ coordinates $(x,y)$; if this is true, then $(x',y',z')$ lies on the surface of the disk, not inside of it.
Mar
3
asked Several questions concerning Alexander's Theorem
Mar
1
comment Inclusions in typologies induced by euclidean and square metric
Right, so, think about it like this: $d$ and $\rho$ are two "measuring systems"; maybe $d$ gives you how far apart two points are in inches and $\rho$ tells you how far apart two points are in centimeters. An inch is larger than a centimeter, so if I wanted to look at all points within 1 unit of $x$, any point which is within one centimeter of $x$ is certainly within one inch of $x$
Mar
1
accepted Smooth structure after surgery
Mar
1
answered Prove that if f is continuous, than its borel function.
Mar
1
comment Inclusions in typologies induced by euclidean and square metric
What is it you're finding conceptually difficult about this result? Try drawing a picture of both "balls" in $\mathbb{R}^2$.
Mar
1
awarded  Curious
Feb
28
asked Smooth structure after surgery
Feb
25
revised Analytic solution to diffuclt integral
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