Henno Brandsma
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 2h reviewed Edit Proof verification: Munkres Theorem 22.1 2h revised Proof verification: Munkres Theorem 22.1 Little fix. 7h answered How to prove any closed set in $\mathbb{R}$ is $G_\delta$ 7h comment How to show that countable union of $F_\sigma$ is $F_\sigma$ The $U_{i,j}$ should be closed, not open. 10h comment How $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots =\ln 2$? Use Euler's criterion (sequence is decreasing in absolute value and alternating) to see that the series $\sum_n \frac{(-1)^n}{n}$ converges. Then Abel's theorem says that this is indeed the value for $x=1$. 10h revised How $1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\cdots =\ln 2$? deleted 21 characters in body 11h comment I like to know if there is approximated expression of something The right hand side is "almost" $e^x$, so this expression should be close to $1 = e^{-x}e^{x}$.. 11h answered Find a unique value for $d$ in $(d \cdot e) \pmod{F} \equiv 1$ 13h comment Is it possible to construct Hausdorff compact topology on every set? Note that $Y$ is discrete and $X$ is its one-point compactification (if $Y$ is infinite). 1d revised Showing that $Im(L^*)=(Ker\: L)^\perp \space \:\mathrm and \:\:Ker(L^*)=(Im\: L)^\perp$ edited tags 1d comment True or False: there is a space $X$ such that $S^1$ is homeomorphic to $X\times X$ @Szmagpie No, it's not that hard, I can write a proof as an alternative answer tomorrow, time permitting. It uses basic connectedness arguments. But the algebraic topology approach is also instructive. Both show ideas that are more widely applicable. 1d revised Relation betwen the base of a product topology and the bases of the topological spaces added 1 character in body 1d answered Relation betwen the base of a product topology and the bases of the topological spaces 1d comment Is the space of subsets of $\mathbb R^n$ with the Hausdorff metric separable? The topology the Hausdorff metric generates is actually also known as the Vietoris topology, and for this it's also quite easy to see the separability. But this comes at a cost: prove that the metric topology and it coincide. The benefit is that in the Vietoris topology is often easier to some properties like connectedness etc. 1d comment Property of compact metric space Note that we only need that $A$ is compact, not that $X$ is. 1d revised Property of compact metric space 2 typos 2d comment If $d_1$, $d_2$ are metrics on $X$ find a relationship between $\tau_1$ and $\tau_2$. E.g. $d_1$ could be the discrete metric, and $d_2$ the usual metric on the reals. 2d answered Accumulation point implies strict limit point? 2d revised Accumulation point implies strict limit point? Latex plus some spelling 2d comment Help finding paper from the 1920's You'd have to go to a library, if the papers have not been scanned. Some journals have started doing that, scanning old issues and putting them online. Rend. Del. Circa. Math. di Palermo probably has not. I'm not close to one...