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2d
answered Show that $\phi_{y,\epsilon} \in D(\mathbb{R^m})$
Feb
10
comment Is $C[0,1]$ reflexive?
This implies that $C[0,1]$ isn't reflexive because reflexivity of $X^*$ implies that of $X$.
Feb
4
comment Is $C_0(\mathbb{R})$ a Banach space?
$C(\mathbb R)$ is not a Banach space: The supremum "norm" is not a normed because it is not real valued. You can make $C(\mathbb R)$ a complete metric space under uniform convergence by $D(f,g)=\sup\lbrace \min\lbrace |f(x)-g(x)|,1\rbrace: x\in\mathbb R\rbrace$.
Feb
2
answered 6.5 theorem in Functional Analysis by Rudin about topological vector space and $\mathscr{D(\Omega)}$
Feb
2
comment Convolution operator is normal
Writing this without integrals: $T*Tf=(f *h)*\overline h = f*(h*\overline h)$. So, all you need is $h*\overline h = \overline h *h$.
Feb
1
answered Borel lemma : wikipedia proof
Feb
1
comment Product spaces and open sets
If $A$ or $B$ is empty the product is empty and hence open. You thus need additionally that $A\times B$ is not empty. Btw, If you consider $d((x,y),(a,b))= \max \lbrace d_1(x,a), d_2(y,b)$ instead of the sum you get an equivalent metric such that balls in $X\times Y$ are exactly products of balls.
Jan
31
comment If we had a complete metric space with no isolated points, then singular points are nowhere dense
You said that I showed that $\lbrace x\rbrace$ is open. Of course, $x$ is then an interior point of $\overline{\lbrace x\rbrace}$.
Jan
29
comment If we had a complete metric space with no isolated points, then singular points are nowhere dense
No, this shows that $\lbrace x\rbrace$ is somewhere dense if $x$ is isolated. By definition, a set is somewhere dense if its closure contains interior points.
Jan
29
answered If we had a complete metric space with no isolated points, then singular points are nowhere dense
Jan
25
revised Prove that Helley Theorem is not true in $L^{\infty}[0,1]$
fixed grammar
Jan
25
answered Prove that Helley Theorem is not true in $L^{\infty}[0,1]$
Jan
19
answered Are $C^k[0,1]$, with the $C^k$ norm, distinct as Banach spaces?
Jan
18
comment Are $C^k[0,1]$, with the $C^k$ norm, distinct as Banach spaces?
Perhaps even simpler: At least for real valued functions the unit ball of $C^0$ has only two extreme points but the one of $\mathbb R \oplus C^0$ has (at least) four.
Jan
18
answered Is $C^1([0, 1], E)$ dense in $C([0, 1], E)$ for a general Banach-space $E$?
Jan
18
comment Are $C^k[0,1]$, with the $C^k$ norm, distinct as Banach spaces?
Just an idea: Is $\mathbb R \oplus\mathbb R^2$ (where $\mathbb R^n$ is endowed with the maximum norm and $\oplus$ with the sum of the norms) isometric to a subspace of $\mathbb R^4$? The unit ball of $\mathbb R \oplus\mathbb R^2$ has 6 extreme points but I don't know about subspaces of $\mathbb R^4$.
Jan
18
comment Sequence in $l^p$ but not $l^q$ for all $q<p$
math.stackexchange.com/questions/480807/…
Jan
18
comment Complete as a semimetric space but not as a topological group
Did you try to pass to the quotient metric?
Jan
14
answered Functionals on locally convex space of complex polynomials
Jan
14
comment Complete as a semimetric space but not as a topological group
@user284331 What do you think about this answer?