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Apr
1
comment Why is $\text{Exterior}(A) = \text{int}(A^c) = \text{cl}(A)^c$?
@MichaelBurr No problem.
Apr
1
comment Why is $\text{Exterior}(A) = \text{int}(A^c) = \text{cl}(A)^c$?
@MichaelBurr Sure. But there are different definitions of closure and interior out there, so I asked.
Apr
1
comment Intersection of nested compact sets in a Hausdorff space
Then $X = \bigcap_{i=1}^n U_i = U_n$ (the $U_n$ are increasing). But $U_n = X$ gives $X_n = \emptyset$, which is wrong. (If $x \in X$, then $f^{n-1}(x) \in X_n$.
Apr
1
comment Why is $\text{Exterior}(A) = \text{int}(A^c) = \text{cl}(A)^c$?
How do you define $A^°$ and $\bar A$?
Mar
25
comment Is there a way to calculate absurdly high powers?
You start from 1 ... usually
Mar
24
comment Can I found $U$, $W$, and $X$ subspace in $V$ which satisfies $(U\cap X)+(W \cap X)\subset(U+W)\cap X.$
What do you denoe by $\subset$? A proper subset, I suppose.
Mar
23
comment How To differentiate this integral
@Vim edited. $ $
Mar
23
comment Hölder space continuously embeds into $L^2$ space?
$\|f\|_{C^{0,\alpha}} = \|f\|_{C^0} + [f]_{C^{0,\alpha}}$
Mar
23
comment Hölder space continuously embeds into $L^2$ space?
@Ian $$ \|f\|_{C^0} \le \|f\|_{C^{0,\alpha}}$$ holds. And we need it that way :)
Mar
23
comment Mapping, relations and logical expressions
And probably (check your definitions) $\underline 3 = \{1,2,3\} $.
Mar
22
comment noncommutative ring with unity..
@user26857 Thx, corrected.
Mar
22
comment Verifying if a function is a.e. equal to a continuous function then it is continuous a.e.
Yes. Although $f$ does a.e. equal the continuous function $0$, $f$ is nowhere continuous.
Mar
22
comment Are there any non-trival sequences which satisfy these conditions?
$a_k = 1$ for finitely many $k$ and $a_k = 0$ otherwise provides more solutions.
Mar
22
comment Mapping, relations and logical expressions
@AndresMejia Yes. And $$ 3 \times 3 = \{(0,0), (0,1), (1,0), (2,0), (0,2), (1,1), (2,1), (1,2), (2,2) \} $$
Mar
22
comment Mapping, relations and logical expressions
And what are the elements of $3$? Or do you by any chance, mean $\{1,2,3\} \times \{1,2,3\}$?
Mar
22
comment Mapping, relations and logical expressions
What do you mean by the set $3$? Usually, one has $3 = \{0,1,2\}$, so $\alpha \subseteq 4 \times 4$...
Mar
22
comment Find $b$ such that $\log_b(x)$ and $\log_b(y)$ are integers.
@SimpleArt As both equal $b$.
Mar
22
comment Two congruent segments does have the same length?
If I recall correctly, we define length in axiomatic geometry by taking the segments modulo congruence. That is the set of possible length is $$ L = \{\text{segments}\}/\cong $$ and the length of a particular segment is the class of it modulo congruence: Hence, obviously, by definition of length, not of congruence, your claim is true.
Mar
22
comment Prove the product of two $W_0^{1,p}$ functions gives another $W_0^{1,p}$ function if $p>n$
It is not true that $$\def\n#1{\left\|#1\right\|_{W^{1,p}}}\n{uv} \le \n u \n v $$
Mar
22
comment convolution: how can I show that $(y*f)'(t) = (y'*f)(t) + y(0)f(t)$
I did not leave off any steps and added something regarding your mistakes.