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 Jan 16 awarded Yearling Jan 14 comment Orientation preserving and orientation reserving of a parameterisation of a curve $u'(t)\geqslant 0$ or $u'(t)\leqslant 0$, right? Dec 5 comment Group Theory: Show that $G/Z(G) \cong Inn(G)$? Use the first isomorphism theorem. Nov 16 comment Characterize continuous functions $f : X → Y$ for which $f^{− 1} ( \{ a\} )$ is open @Nex Yeah, I know :) Nov 16 comment Characterize continuous functions $f : X → Y$ for which $f^{− 1} ( \{ a\} )$ is open @Nex He's probably asumming points are closed in $Y$. Nov 16 comment Characterize continuous functions $f : X → Y$ for which $f^{− 1} ( \{ a\} )$ is open What happens if a set is both open and closed? Nov 2 comment Solving a polynomial with complex coefficients Let $w=z^3$. Solve $w^2+(2i-1)w-1-i$ and then find $z$. Oct 18 comment determine the frontier What do you mean by frontier? In any case, note that every real number is the limit of a sequence of irrational numbers. Oct 18 answered Modulus of n-tuples? Oct 18 revised Which kind of problems of Set Theory are solved in which way? Delete set-theory tag Oct 18 suggested approved edit on Which kind of problems of Set Theory are solved in which way? Oct 12 comment Show that $\lim_{n\to \infty} (\sqrt{n+1} - \sqrt n) = 0$ using the definition of a limit Which sign change? I just used that $a^2-b^2=(a-b)(a+b)$. For the limit, given any $\varepsilon$, you need to find $N$ such that $|\sqrt{n+1}-\sqrt n|<\varepsilon$ if $n>N$. If you find $N$ for $1/(2\sqrt n)$ you're done by what's above. Oct 12 answered Show that $\lim_{n\to \infty} (\sqrt{n+1} - \sqrt n) = 0$ using the definition of a limit Oct 4 answered Describing the image of the complex set $G = \{ z = x+iy \mid x^2 + y^2 + 2x + 2y + 1 = 0\}$ Oct 1 comment Prove that $\gcd(g_a,g_b) = 1$ given that for $n \in Z^{\geq 0}$, define $g_n = 2^{2^n} + 1$ math.stackexchange.com/questions/1458929/… Sep 28 answered A locally injection is an injection? Aug 7 comment General Isomorphism, for all algebraic structures The "homomorphisms" in the category of topological spaces are the continuous functions, and they do not behave like homomorphisms in groups, rings,... See here. Aug 7 comment General Isomorphism, for all algebraic structures Take $f$ from $[0,2\pi)$ to the unit circle in $\Bbb R^2$ defined by $f(t)=(\cos(t),\sin(t))$. Jul 20 comment Bounded Matrix-Vector Multiplication $Ax$ is a vector, so its norm $\| Ax\|$ is a well-defined real number. If you are asking about the boundedness of the set $B=\{\| Ax\| :x\in \Bbb R^p\}$, then $B$ is bounded if and only if $A=0$. Jul 16 comment Is every compact set in $\mathbb R^2$ a continuous image of some compact set of $\mathbb R$? @Siminore This is Theorem 30.7 of Willard's General Topology.