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Feb
7
comment Nonlinear operator sends bounded set to relatively compact set
How do we ensure the same $M$ works for all the $v\in B$?
Feb
3
comment Example of Spherical Element (Simplicial Homotopy)
Thanks! I think I am starting to get it. So if $x$ is spherical, all the vertices and edges of $x$ are identified into a single point? By your answer that is a sufficient condition, is it also a necessary condition?
Feb
1
comment Example of Spherical Element (Simplicial Homotopy)
I missed out the key word "fibrant" or Kan complex. So $X$ is a simplicial set with a choice of a basepoint, it is also fibrant (Kan complex).
Jan
28
comment Form of elements in closed linear span
Thanks, can you elaborate a bit on how to use Bessel's inequality? When I tried using it I got $\sum|\langle x,x_j\rangle|^2\leq\|x\|^2$
Jan
27
comment Fibrant (Kan complex) geometric meaning
Thanks for introducing Friedman's paper
Jan
26
comment Matching faces in Simplicial Set theory
@Zhenlin In other words, they are "adjacent" or "touching each other"?
Jan
25
comment How did Von Neumann think of the formula for scalar product?
@littleO thanks I get it now
Jan
11
comment Analytic Isomorphism from open region to upper half plane
Just to check, do you mean $f(z)=\frac{-2}{1+z}+1$?
Jan
5
comment Analytic Isomorphism from open region to upper half plane
Thanks for your help. Which topic of complex analysis should I read up to learn more of this?
Jan
3
comment Hatcher Corollary 4.12
@MikeMiller No problem, thanks for your help
Jan
3
comment Hatcher Corollary 4.12
@MikeMiller Yes, I was saying the relative groups were automatically zero (due to the n-connectedness).
Jan
3
comment Hatcher Corollary 4.12
@MikeMiller What I deduced is since $(X,X^n)$ is n-connected, $\pi_n(X,X^n,x_0)=0$. Thus, applying the boundary map $\partial$ leads to $\pi_{n-1}(X^n,x_0)=0$. And so on, all the later terms are zero?
Jan
2
comment Zeroth homotopy group: what exactly is it?
@Mauro I just read up: it is the set of two points at the end of a line segment
Jan
2
comment Zeroth homotopy group: what exactly is it?
@MarianoSuárez-Alvarez thanks for your answer! Why is $\pi_0$ not a group?
Dec
18
comment Alternative isomorphism map to prove R-module isomorphism
@SpamIAm Ah I think I see it, the answer can be 3 or 1, so it is not well defined. Thanks for the enlightenment.
Dec
18
comment Alternative isomorphism map to prove R-module isomorphism
@SpamIAm Thanks. I am quite confused regarding well-definedness of tensor products. In undergrad, well-defined was mainly for coset representatives. I.e. If I defined a map $f:\mathbb{Z}/2\to\mathbb{Z}/2$ by $f(0+2\mathbb{Z})=0+2\mathbb{Z}$ and similarly for $f(1+2\mathbb{Z})=1+2\mathbb{Z}$, I believe that would be automatically well-defined, no? I wouldn't have to worry about $1+4$ and $1+6$ as two different representatives for $1+2\mathbb{Z}$? Thanks for enlightening me!
Dec
9
comment What is theta value?
Yes it is related to the polar coordinates
Dec
1
comment Induced Isomorphism on 2nd Homology Group
Thanks for your answer! Just to ask which textbook do you recommend for learning Homology?
Dec
1
comment Induced Isomorphism on 2nd Homology Group
I googled and found it is trivial group. I haven't learnt homotopy group though.
Nov
29
comment Continuous map from Projective Plane to Torus
Thanks! Just to ask what do you mean by "and every map is induced" in the last part?