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Apr
8
comment Is $(-\infty, 0]$ closed in $\mathbb{R}$?
Obviously yes..
Mar
31
comment An infinite sum based on the mod-parity of Euler's totient function
Anyway, by a theorem of Dence and Pomerance, the number of integers in $n \in [1,x]$ such that $12 \mid \phi(x)$ is equal to $(1+o(1))x$ [oh, they derive also other class residues mod 12] ..
Mar
31
answered Can we find two numbers from $n+2$ numbers chosen from $\{1,2,3,\cdots\}$?
Mar
30
answered Let $n,r,a$ be positive integers with g.c.d.$(a,d)=1$ , does there exist integer $m$ relatively prime to $n$ such that $d|m-a$?
Mar
29
revised Showing a function can not be continuous.
added 1 character in body
Mar
29
revised Showing a function can not be continuous.
added 2 characters in body
Mar
29
answered Showing a function can not be continuous.
Mar
29
accepted The image of a segment is not dense into a square
Mar
29
comment The image of a segment is not dense into a square
Right, I forgot to add "with non-empty interior"; let us say, the cube in $\mathbf{R}^3$ is not homemorphic to a closed square in $\mathbf{R}^3$..
Mar
29
comment The image of a segment is not dense into a square
I agree, thanks Clement and Amitai; trying to generalize to higher dimensions, is it possible to prove on the same line of reasoning that a compact subset of $\mathbf{R}^3$ is not homeomorphic to a closed square in the plane $x=0$ of $\mathbf{R}^3$?
Mar
29
asked The image of a segment is not dense into a square
Mar
29
accepted Subset of open set and subset of its bourdary is open
Mar
29
comment Subset of open set and subset of its bourdary is open
Now it works, well :)
Mar
29
comment Subset of open set and subset of its bourdary is open
Well, $B$ should be the bourdary of $A$, not the bourdary of $A^\prime$..
Mar
29
revised Subset of open set and subset of its bourdary is open
deleted 10 characters in body
Mar
29
comment Subset of open set and subset of its bourdary is open
Why $(0,0) \in B$?
Mar
29
comment An infinite sum based on the mod-parity of Euler's totient function
Why do you think it should be a relevant sum in number theory?
Mar
29
asked Subset of open set and subset of its bourdary is open
Mar
20
awarded  Benefactor
Mar
19
accepted Continuous image of convex hulls