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I'm a student of mathematics in Germany.


Apr
9
revised Determining injectivity and surjectivity
added 10 characters in body
Apr
9
revised Determining injectivity and surjectivity
edited tags
Apr
9
comment Determining injectivity and surjectivity
You really need to know the domains and codomains to decide this.
Apr
9
comment Continuity of the sum of continuous functions
Prove $B(a,δ) × B(b,δ) ⊂ (+)^{-1}[B(\underline{a+b},ε)]$ instead.
Apr
8
comment Continuity of the sum of continuous functions
@Jens I didn’t characterize the preimage of an open ball around $c$, but I instead said that any point in this preimage has an open neighbourhood within the preimage. The cartesian products of open sets in $ℝ$ is open in $ℝ × ℝ$. I firmly believe you can show the continuity of the absolute value yourself using the same trick. Ask again if you couldn’t manage to do so.
Apr
8
revised Prove that $f$ is constant if $f'=0$
added 13 characters in body
Apr
8
answered Prove that $f$ is constant if $f'=0$
Apr
8
comment Prove that $f$ is constant if $f'=0$
You can do this by showing $\exp(z) \exp(c-z) = \exp(z + (c-z)) = \exp(c)$, using the functional equation $\exp(a+b) = \exp(a)\exp(b)$ (i.e. $\exp \colon ℂ → ℂ^×$ is a group homomorphism). The question statement is true nevertheless (assuming domains are meant to be connected), and I think there are several generalisations which should be easy to prove.
Apr
8
comment Prove that $f$ is constant if $f'=0$
Why do you want to show that and how far did you come?
Apr
8
comment Continuity of the sum of continuous functions
@Jens Is that okay?
Apr
8
revised Continuity of the sum of continuous functions
explained in more detail as requested in a comment
Apr
8
answered Continuity of the sum of continuous functions
Apr
8
comment Possible logical meanings of mathematical operations
In $\mathbb{F}_2 = ℤ/2ℤ$, if you interpret zero as false and one as true, “$+$” (and “$-$”) corresponds to exclusive or and “$·$” corresponds to and.
Apr
7
comment Does this topology on the dual have a name
Wht did you choose $ℂ$ to be the codomain of the $p_x$?
Apr
7
comment Are there non-surjective homeomorphisms?
By that phrase, they just mean homeomorphisms $X → X$, i.e. whose domain and codomain is $X$.
Apr
6
comment Notation for partial function set.
@AsafKaragila Wow. By itself, this is a very useless comment, but it probably carries some weight because you know a lot of mathematics and are into logic and set theory.
Apr
6
comment Vectorspace subspace proof
@user140831 Actually, I don’t think this answers the question entirely and I’m not sure if I thought of the whole solution when posting this. Maybe I was a bit confused. And maybe you’ve already done the rest, but if not, let me add: Any (non-zero) vector not contained in $W$ can be used to extend the base as the one to be left out later on. This proves $W^c ⊂ Y^c$.
Apr
6
comment Question about integration in $\mathbb{R}^n$
So we’re talking Riemann integrable here?
Apr
6
answered Vectorspace subspace proof
Apr
6
awarded  Pundit