4,024 reputation
520
bio website
location
age
visits member for 2 years, 2 months
seen 2 days ago

Dec
11
comment Paul Erdos's Two-Line Functional Analysis Proof
Sure would be nice to know what the result was (and the contents of Erdős's proof). Any update on that?
Dec
11
comment
Two things I would want in a moderator are transparency and an even temper. The exchange I read here doesn't give me much confidence in either for this candidate.
Dec
11
comment Conjecture about $A f(x) = f(g(x)) + f(h(x))$
I'm not following this question. Suppose $f$ is a constant function, say $f = 1$ everywhere, and $A = 1.5$. The expression $f(g(x)) + f(h(x))$ is $2$ everywhere and $f(g(x)) - f(h(x))$ is $0$ everywhere. So what gives?
Dec
11
comment Are two bimodules isomomorphic as left and right modules also isomorphic as bimodules?
This isn't really a research level question, but you might consider a situation where $R$ is an $R$-bimodule in the standard way, vs. a situation where $R$ is a left module in the standard way but a right module in a twisted way, twisted by an involution on the ring. Think of a familiar ring or field with an involution, and you should be on your way.
Dec
10
awarded  Caucus
Dec
8
awarded  Revival
Dec
8
answered Complete but not cocomplete category
Nov
21
answered Is there any general method of finding the lower bound of $x$ that satisfy the inequality?
Nov
19
comment Are mathematical articles on Wikipedia reliable?
@Sanath I'd give it a little more time before you proclaim to people that you are a mathematician. Even Paul Halmos titled his automathography "I Want to Be a Mathematician" (emphasis mine), and that attitude sounds about right. :-)
Nov
18
comment Exercise 12. 8. 7, page 510 0f Grillet's Abstract Algebra
Well, you have an answer. If this answer was helpful to you, then please consider upvoting and accepting (there's a box you can check for accepting an answer). Thanks.
Nov
17
comment Exercise 12. 8. 7, page 510 0f Grillet's Abstract Algebra
On a different topic: please do not crosspost. I saw the same question posted to MathOverflow (where it is now closed) -- the problem with crossposting is that it leads to duplication of effort, hence a waste of time for busy professionals. Thanks.
Nov
17
answered Exercise 12. 8. 7, page 510 0f Grillet's Abstract Algebra
Nov
17
comment Literature on ellipses
One pointer is that arc length along ellipses are computable in terms of elliptic integrals and elliptic functions, a huge literature going back to the 19th century. Perhaps en.wikipedia.org/wiki/Elliptic_integral can help get you started.
Nov
16
comment For every connected space X and an open cover U, every two points has a simple chain containing them
(You probably shouldn't use the word "group" because that has a meaning in algebra which makes it confusing here.) I suggest that you read my answer again very carefully, checking that the equivalence classes are open (I didn't say "connected"; let's not even worry about that). If there is more than one equivalence class, then pick a point $a$ in one such class $V$, pick a point $b$ in another, let $W$ be the union of all the equivalence classes except $V$. Then $V$ and $W$ are nonempty, open, disjoint, and cover the space, contradiction.
Nov
16
comment For every connected space X and an open cover U, every two points has a simple chain containing them
I do not understand your question. Chains are finite by definition. But let me offer another way of saying it. Given a cover, let $R$ be the relation where $xRy$ if $x$ and $y$ both belong to an element $U$ of the cover. This $R$ is reflexive and symmetric. Now consider the transitive closure $\sim$ of $R$, where $x \sim y$ if there are $x_0, \ldots, x_n$ with $x = x_0$, $y = x_n$, and $x_i R x_{i+1}$. This $\sim$ is an equivalence relation and is what I meant by $\sim_{\mathcal{C}}$ in my answer. Apply my reasoning to this $\sim$.
Nov
16
answered For every connected space X and an open cover U, every two points has a simple chain containing them
Nov
10
comment How to write notation for this function?
The content of Paul's answer, inasmuch as it answers your question, is that some people write $\lambda\; x. g(h(c, x; X_0))$. (You don't actually "need" much theory of lambda calculus.) Others might write $g(h(c, -; X_0))$.
Oct
30
comment complete compact open topology
If $X$ is any metric space and $Y$ is a compact Hausdorff space, then the compact-open topology on the space of continuous maps $Y \to X$ agrees with the sup-norm metric topology. This is a classical fact. Then apply this to $Y = [0, 1]$. (And if $Y$ is CH and $X$ is a complete metric space, then the sup-norm metric space of continuous maps $Y \to X$ is complete.) I think all this is in Kelley's topology book, and even generalized to the context of uniform spaces.
Oct
30
comment complete compact open topology
And then check that this metric topology on $PX$ is the same as the compact-open topology (which is certainly true and not hard).
Oct
13
comment Derivative of a projective transformation
I would interpret the derivative at a point as a linear transformation between tangent spaces, and the derivative of a smooth map generally as an induced map between tangent bundles. But I don't think MO is the right venue, so I'm migrating. Incidentally: doesn't the induced map between projective spaces make sense only if the matrix is invertible?