Reputation
1,271
Next privilege 2,000 Rep.
Edit questions and answers
Badges
3 12
Newest
 Yearling
Impact
~29k people reached

Jun
23
awarded  Yearling
Jun
14
awarded  Tumbleweed
Jun
7
asked free algebras over noncommutative rings
May
24
comment Generator of group $D_n$
Try this: pick one side of the polygon, and think about where a symmetry could take that side. I think that will tell you that the symmetry is either a rotation or a rotation with a reflection.
May
24
answered Extreme value theorem, without Heine Borel.
May
24
comment Try to use Homogeous space Characterize the space of all lines in the plane .
Presumably you prefer to find a smooth structure which is compatible with some other information such as the symmetries of the plane. Otherwise, you could simply observe that the set of straight lines can be put in one-to-one correspondence with the real numbers, and then use the smooth manifold structure on $\mathbb{R}$.
May
24
comment Try to use Homogeous space Characterize the space of all lines in the plane .
It looks like Theorem 21.20 gives your result directly; you don't need to know anything about $G / G_m$. What do you feel is missing from that argument?
May
13
comment Questions about homomorphisms?
"But why are the kernels ideals": people thinking about rings realized that ideals are important, and that kernels are important, and that these are basically the same thing.
May
13
answered Questions about homomorphisms?
May
7
answered Comparing Open Bases and Covers
May
7
comment Finite abelian groups of order 100
Hint: what's the order of the group $Z_2 \times Z_5$? That order depends on $2$ and $5$ in a simple way.
May
6
comment Preserving compactness and connectedness implies continuity for functions between locally connected, locally compact spaces?
I think you have to admit that between me and @BrianMScott, your original question is now answered...
May
1
answered Preserving compactness and connectedness implies continuity for functions between locally connected, locally compact spaces?
Apr
28
comment Suppose $A$ is a nonempty subset of $\mathbb{R}^n$. Prove that if $A$ is both open and closed, then A=Rn.
There's no obvious notion of "bounded above" or "sup" in $\mathbb{R}^2$. However, @BolzWeir's argument is good if you know that $\mathbb{R}$ is connected and that products preserve connectedness.
Apr
28
comment Proving that two equivalence classes are disjoint?
Yes, that's right. Now you have to show that $1 R a$ and $0 R a$ can't both be true.
Apr
28
comment Proving that two equivalence classes are disjoint?
$0^{\overline{0}}$ does not appear to mean anything; just say $\overline{0}$ and $\overline{1}$.
Apr
21
comment How to scale a random integer in $[A,B]$ and produce a random integer in $[C,D]$
I added some details, see if that helps.
Apr
21
revised How to scale a random integer in $[A,B]$ and produce a random integer in $[C,D]$
add details on specific example and uniform distribution
Apr
20
comment Am I a toroid or not?
Many of us increase our genus with body piercings.
Apr
20
comment How to scale a random integer in $[A,B]$ and produce a random integer in $[C,D]$
Yes, if you set the output range to be from $0$ to $2^{22} - 1$ or from $1$ to $2^{22}$, the range size will be $2^{22}$ and it's easy to solve. For example, if the input is from $-2^{31}$ to $2^{31} - 1$ and the output is from $0$ to $2^{22} - 1$, $y = (x + 2^{31}) \mod 2^{22}$ works.