3,325 reputation
516
bio website
location
age
visits member for 1 year, 7 months
seen 18 mins ago

I'm a graduate student of mathematics in Germany.


Mar
8
answered Local ring with principal maximal ideal
Mar
8
comment Proper functions
$\sin \colon ℂ → ℂ$ is not proper as it maps a non-compact set to a compact one. Nontrivial polynomial functions $ℂ → ℂ$ are proper because the preimage of compact set in $ℂ$ is the preimage of a bounded set which is closed in $ℂ$. As polynomial functions are continuous, these preimages are closed, and it is well known that nontrivial polynomial functions tend to infinity as their arguments grow, so a preimage of a bounded set is closed. Therefore, preimages of bounded closet sets are bounded and closed. Therefore, preimages of compact sets are compact.
Mar
8
answered Supposed X and Y are metric spaces and $f:X \rightarrow Y$ and $g:X \rightarrow Y$ are continuous prove $\{x \in X:f(x)=g(x)\} $ is a closed set
Mar
8
comment Every function from a discrete subset is continuous
This greatly depends on your definitions of discrete and of continuous. What are they?
Mar
8
revised Limit of inverse function
added 136 characters in body
Mar
8
comment Limit of inverse function
@Awesome Yeah, right. Either you have something to contribute or not. If you say you don’t have, then don’t say anything at all. It’s noise.
Mar
8
answered Limit of inverse function
Mar
8
comment Limit of inverse function
@Awesome Why and how does this help?
Mar
8
comment Limit of inverse function
@Awesome Which limits are equal, what makes no difference and how does that follow?
Mar
8
comment Limit of inverse function
@Awesome You’re assuming continuity.
Mar
8
answered $\lim \sup$ of a sequence
Mar
6
revised Group Theory Questions
added 29 characters in body
Mar
6
answered Group Theory Questions
Mar
6
comment What is larger x and what is smaller x?
Wait, … what? What do you mean by "larger x"? Larger than what?
Mar
6
comment How is the following set closed?
@EmanuelePaolini Well, $S_n(U)$ is only defined for $U ∈ A$. Or is it $U ⊂ A$ and in the definition of $S_n (U)$ it should read $B(x,1/n) ∈ U$? You should clarify this, Raghav.
Mar
6
comment How is the following set closed?
Does the well-ordering of $A$ ever come into play?
Mar
6
comment What is the “opposite” of a forgetful functor?
I take it, the monoid $M$ you are using is not arbitrary, but dependent on the category $C$? This is not something like the forgetful functor which forgets the structure of the objects and morphisms, but it’s a functor which forgets a lot of the structure of the category itself. The functor you are looking for maybe gives rise to a “forgetful” endofunctor $\mathrm{Cat} → \mathrm{Mon}$, though.
Mar
6
comment When does connected space imply locally connectness?
Being connected is very different from being locally connected. I think, this is very broad question.
Mar
6
comment Proving inverse of two matrices
$J_n^{-1}$ doesn’t exist as $J_n$ is not invertible.
Mar
6
comment Gauss elimination
Am I the only one to notice that these questions pop up a lot lately (including the attempted [tex]-[/tex]-syntax)?