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1d
comment closed subspace of a linear space
Yes, that's one characterization.
1d
comment Prove dimension finiteness for a separable subspace of $L^\infty(0,1)$.
You don't, since that's not true.
Feb
3
comment Subspace of a weakly sequentially complete is weakly sequentially complete
Yes. See Norbert's answer here.
Jan
31
comment If two subspaces have the same basis are they equal?
Yes, that's right.
Jan
30
awarded  Enlightened
Jan
30
awarded  Nice Answer
Jan
28
answered Give an example of two closed disjoint sets $F$ and $G$ (subsets of $\mathbb{R}$) such that $\inf\{|x-y|; x\in F, y\in G\}=0$.
Jan
28
comment Give an example of two closed disjoint sets $F$ and $G$ (subsets of $\mathbb{R}$) such that $\inf\{|x-y|; x\in F, y\in G\}=0$.
$\{1,2,\ldots\}$ and $\{1+1/2,2+1/3,\ldots\}$.
Jan
27
comment How Many Circles go Through 3 Distinct Points of $\mathbb{R}^2 $
The perpendicular bisector of a chord of a circle passes through the center of the circle.
Jan
23
comment Why is my counterexample of this Theorem wrong or invalid?
$3$ is not every epsilon.
Jan
22
comment Good reference for Fourier Analysis
@user254665 Did you mean Zygmund?
Jan
19
comment When does convergence of Cesàro mean imply convergence
@user254665 The question was edited; the comment is no longer relevant.
Jan
18
revised How do I determine the graph of functions involving radicals?
edited tags
Jan
14
comment $(f_n)$ in $L^p(\Omega)$ satisfying $f_n(x) \to f(x)$ a.e. and $\|f_n\|_p \to \|f\|_p$, then $\|f_n - f\|_p \to 0$?
See this.
Jan
11
comment Pointwise and weakly convergent limits are the same
See this.
Jan
10
revised Determine whether a function series is uniformly convergent
edited tags
Jan
10
comment Proving an integral is uniformly continuous: $f(x)=\int_{-\infty}^{x} e^{\frac{-t^2}{2}} dt$
$|f(x)-f(y)|\le\int_x^y | e^{-t^2/2} |\,dt\le \int_x^y 1\,dt$.
Jan
10
revised Proving an integral is uniformly continuous: $f(x)=\int_{-\infty}^{x} e^{\frac{-t^2}{2}} dt$
edited tags
Jan
10
comment Is $ f\left(x\right) =\int^{x}_{0}\sin( e^{t^{2}})\,\mathrm{d}t$ uniformly continuous?
$|f(x)-f(y)|=\Bigl|\int_x^y \sin (e^{t^2})\,dx \Bigr|\le\Bigl|\int_x^y 1\,dx \Bigr|\le|x-y|$.
Jan
9
comment How many sequences of rational numbers converging to 1 are there?
If $x_n\rightarrow0$, then $1\pm x_n\rightarrow 1$ for any choice of signs.