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Doing math.


Oct
20
comment The Complex projective space is homeomorphic to the n-sphere
What definition of the complex projective space do you use?
Oct
15
comment Question about the closure of a set
@Luis: That sequence does not have a limit.
Oct
15
answered Question about the closure of a set
Oct
15
reviewed Approve suggested edit on Question about the closure of a set
Oct
2
comment The set of rational numbers in the interval $(0,1)$ cannot be expressed as the intersection of a countable collection of open sets
@YiorgosS.Smyrlis. Got it. Thanks.
Oct
2
comment The set of rational numbers in the interval $(0,1)$ cannot be expressed as the intersection of a countable collection of open sets
@YiorgosS.Smyrlis: Why do $U_{n}$ have to be dense? The statement only says that rationals in $(0,1)$ can not be expressed as a countable intersection of open sets, not necessarily dense ones.
Sep
30
awarded  Explainer
Sep
28
answered Prove that $\{x_{n}\} \subseteq A$ a Cauchy sequence $\Rightarrow$ $\{f(x_{n}\}\} \subseteq y$ is a Cauchy sequence.
Sep
12
comment Why is differential geometry called differential geometry?
Usually the Riemannian metric of a smooth manifold captures it's geometric properties such as curvatures and angles. One doesn't need to integrate on the manifold to capture these notions.
Sep
12
revised Why is differential geometry called differential geometry?
[Edit removed during grace period]
Sep
12
answered Why is differential geometry called differential geometry?
Sep
7
answered Does $V_1,V_2,V_3$ span $R^4$
Jul
2
awarded  Curious
May
28
comment Research Area Choice: PDE vs Optimization
What type of industry would you like to consider outside of academia? Bear in mind that PDEs are used in finance too.
May
15
comment How to prove or disprove $P(\overline A) = P(U) - P(A)$
Could you clarify what $P(A)$ stands for? And what exactly do you mean by the statement "$U-A$ implies $A\cap \overline{U}$"?
May
15
comment Show that if sup{∑|f(a)|}<∞, then {a∈A:f(a) is not zer0} is countable.
@user140794: Assume that there are infinitely many $a_{1},a_{2},...\in A$ with $f(a_{k})>\frac{1}{n}$ for all $k\in\mathbb{N}$. Then $\sup_{N\in\mathbb{N}}\sum_{k=1}^{N}f(a_{k})=\infty$, which is a contradiction to your assumption. And note for the last part: for absolutely convergent series the order of terms doesn't affect the sum.
May
14
answered Show that if sup{∑|f(a)|}<∞, then {a∈A:f(a) is not zer0} is countable.
May
13
answered Any idea of how to prove this
May
13
comment A subspace of a separable metric space is separable
The goal is not to show that $A$ is dense and countable, as this would not necessarily be true, but rather that $A$ contains a countable dense subset of itself with respect to the subspace topology.
May
13
revised Proving that there is no norm for the space of real-valued sequences making it a complete metric space.
edited tags