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Feb
3
comment Lipschitz Functions
@user119459: The OP says specifically: "Assume that the sequence of functions has a common Lipschitz constant $K$."
Jan
28
comment Geometric interpretation of connection forms, torsion forms, curvature forms, etc
What does it mean (precisely) for two points $x,y \in M$ to be "infinitesimally close" or "close to first order"?
Jan
27
comment $C^{\infty}_{C}(\Omega)$ it is dense in $ W^{1,2}(\Omega)=H^1(\Omega) $ ? I know that it is dense in $H^1_{0}(\Omega).$
@MaoWao: That's a useful fact, thanks. Do you have a reference?
Jan
18
awarded  Good Answer
Dec
22
awarded  Popular Question
Dec
19
awarded  Good Question
Dec
18
awarded  Nice Question
Dec
18
comment Why do we care about two subgroups being conjugate?
@goblin: not necessarily. To endow $G/H_1$ and $G/H_2$ with group structures, then yes, I should have added normality in that line; I was being careless.
Dec
18
comment Why do we care about differential forms? (Confused over construction)
"... why write this as $dx$, which had previously been used to mean an infinitesimal increase in $x$." What exactly, precisely, is meant by an "infinitesimal" increase in $x$? Unless one goes the (somewhat cumbersome) route of "non-standard analysis," there isn't a precise meaning of this -- until one introduces differential forms.
Dec
18
asked Why do we care about two subgroups being conjugate?
Dec
18
reviewed Approve In what sense is this action of $\mathbb R$ on $T$ lifted to an action of $\pi_1(T)\times\mathbb R$ on $\mathbb R^2$?
Dec
15
comment Is the supremum of the closure equal to the supremum of the set?
What do you mean by "$\sup(M) \in \overline{M}$ in general"? Is $\text{sup}(M)$ a real number or an element of $X$? What is the definition of $\sup(M)$?
Dec
15
revised How to prove $d\omega=(\nabla_\mu\omega)_\nu dx^\mu\wedge dx^\nu$ without using coordinates
edited body
Dec
14
answered How to prove $d\omega=(\nabla_\mu\omega)_\nu dx^\mu\wedge dx^\nu$ without using coordinates
Dec
14
answered Does $1^{\infty}=e$ or $1^{\infty}=1$?
Dec
14
answered Partition into “fibers” $f^{-1}(y) \in Y$
Dec
13
comment Why vector field can be the gradient of a function $f$?
To be clear, though, not every vector field on a Riemannian manifold can be written as the gradient of some function.
Dec
13
comment Is there a reason for different nomenclature on Calculus of Variations?
this is a great question; eagerly awaiting good answers
Dec
12
awarded  Favorite Question
Dec
10
revised Let $f_1, f_2: \mathbb{R}^n \to \mathbb{R}$ be lower semicontinuous at $a \in \mathbb{R}^n$. Prove that $f_1+f_2$ is lower semicontinuous at $a$.
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