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 Apr11 awarded Yearling Dec1 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... Jul3 awarded Enlightened Jul3 awarded Nice Answer Jun24 comment The Integral that Stumped Feynman? surely one of your Re's should be an Im? Apr11 awarded Yearling Mar1 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? Dec3 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... Sep22 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 $\mathbb{R}$? Aug24 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). Aug24 comment Define a metric based on a topology i think what you are looking for is the "metrizability" of a topology. Aug13 comment Advice for GRE exam (Surface area of cylinder) i think we really need to see the original question for this one. Jul31 comment Why are topological spaces interesting to study? Actually, Furstenberg's topology on the integers is metrizable with the norm $||n||=(\max\{k\in\mathbb{N}^*:1|n,\dots,1|k\})^{-1}$ May14 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... May8 comment Constructing Points I'm pretty sure we'll need a drawing to help you. Apr11 awarded Yearling Apr10 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? Apr2 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. Apr2 comment Can convergence be seen as a form of continuity? 1) Take $Y=\{x\}$ Mar23 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?