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 Dec 1 comment Is$[0,1] \left\backslash\right. \left\{ 1/n :n \in \mathbb Z^+ \right\}$ compact if given the subspace topology? It's not even closed... Jun 24 comment The Integral that Stumped Feynman? surely one of your Re's should be an Im? Mar 1 comment Is it possible to make a commutative homomorphism image non-commutative? Can't you take $\rho$ and $\tau$ to be the identity morphisms on $G$ and $K$ respectively? Dec 3 comment Nice notation for projection maps If the codomain is clear by context, you could (by abuse of notation) just write $\pi$ for both maps... Sep 22 comment Let $x_0$ $\in \space G$, G is open, and put $F=[x_0,\infty) \cap G^c.$ (a) Prove that $F$ is a non-empty set. Your counterexample clearly works, so something's wrong with this exercise. Maybe you are supposed to be using an alternative topology on $\mathbb{R}$? Aug 24 comment Define a metric based on a topology In many cases $d$ will not exist, but even if it does, at this time we don't know a general method to construct such a $d$ (and as said, once you've found one metrization, you'll have found infinitely many). Aug 24 comment Define a metric based on a topology i think what you are looking for is the "metrizability" of a topology. Aug 13 comment Advice for GRE exam (Surface area of cylinder) i think we really need to see the original question for this one. Jul 31 comment Why are topological spaces interesting to study? Actually, Furstenberg's topology on the integers is metrizable with the norm $||n||=(\max\{k\in\mathbb{N}^*:1|n,\dots,1|k\})^{-1}$ May 14 comment Can a Accumulation Point be an Eigenvalue? In what space is 0 an accumulation point, and what is it accumulated by? Clearly, the zero operator is compact and has eigenvalue 0... May 8 comment Constructing Points I'm pretty sure we'll need a drawing to help you. Apr 10 comment Explaining why we can't “find” an antiderivative of $f(t) = e^{t^2}$. The "general formula for the roots of a polynomial"-problem was solved beautifully by Galois theory; is this problem equally elegantly solved? Apr 2 comment Can convergence be seen as a form of continuity? Oh, i'm sorry, /all/ topological spaces $Y$. I read "is there a toplogical space "Y" s.t....". My bad. Apr 2 comment Can convergence be seen as a form of continuity? 1) Take $Y=\{x\}$ Mar 23 comment How do I prove the following: $f(S\cup T) = f(S) \cup f(T)$ 1. please use latex for math notation. 2. what are your own thoughts? what is your definition of them being equal? Mar 19 comment How do i prove that the reduced row echelon form is unique? By "question", I meant your definition of being in reduced row echelon form. I meant that you never defined what it means for $B$ to be the rref of $A$. Mar 19 comment How do i prove that the reduced row echelon form is unique? You only defined the property of being in reduced row echelon form. This is a yes/no question. I cannot think of a natural definition for uniqueness from your question. Mar 19 comment to show $X$ is disconnected You don't need a concept of a "mother space" to define connectedness - it's all about finding two open subsets $A,B\subset X$ with $A\cap B=\emptyset$ and $A\cup B=X$. Mar 19 comment $g:\mathbb{C}\rightarrow\mathbb{C}$ be analytic and $g(0)\neq 0$ we need to calculate $\frac{1}{2\pi i}\int_{|z|=r>0} f(z)g(z) dz$ Calculate residue at 0 using Laurent series? Mar 10 comment Show that $f(z)$ has no antiderivative in $\,S=\mathbb{C}\setminus \{-i,i\}$ @mrf: Then i think it would be more correct to say "You could've also picked an integral around z=-i, because you'd get similar problems", instead of just "repeat". "Repeat" makes it sounds like they're both necessary.