Brian M. Scott
Reputation
398/400 score
 1h answered Characterize those functions which maps open interval to open interval(s). 1h comment Kunen exercise III.8.21 @Stefan: Surely the order must be $\subseteq$. 3h answered Existence of how many sets is asserted by the axiom of choice in this case? 3h comment Is it possible to construct Hausdorff compact topology on every set? @Asaf: My penmanship is actually rather good, or at any rate was before age and constant typing got to it, but it’s italics, and the upper-case P is somewhere between $P$ and $\mathcal{P}$. I deliberately use something different for power set. (And my calligraphic upper-case P’s depend on the hand and are different yet!) 4h comment Is it possible to construct Hausdorff compact topology on every set? @ForeverMozart: Yes. It’s non-standard, but I’ve always used it, because it looks more like my handwritten power set symbol than any of the other available choices. 4h revised Is it possible to construct Hausdorff compact topology on every set? added 236 characters in body 4h answered Is it possible to construct Hausdorff compact topology on every set? 4h answered Proving Recurrence Relation By Forward Substitution 4h answered What is the coefficient and constant term in the following sequence defined recursively? 11h comment Cantor normal form to compute sums and products of ordinals: $\omega^{\beta} c+\omega^{\beta'} c' = \omega^{\beta'}c'$ if $\beta'>\beta$ @akkarin: $\omega^\beta\cdot c+\omega^{\beta+1}=\omega^\beta\cdot c+\omega^\beta\cdot\omega=\omega^\beta\cdot (c+\omega)=\omega^\beta\cdot \omega= \omega^{\beta+1}$, since $c$ is finite. And $c'\ge 1$, so $\omega^{\beta+1}\cdot c'=\omega^{\beta+1}+\omega^{\beta+1}\cdot(c'-1)$. 12h comment Closed set minus an open set. It is indeed. Now apply that to the rest of $A\setminus B$, and you’ll be in business. 12h comment Closed set minus an open set. $4$ is in $A\setminus B$, but so are four other points. What is $[0,1]\setminus(0,1)$? 12h answered Constructing a metric $\rho$ such that $(\mathbb{R}\setminus \{0\},\rho)$ is a complete metric space 13h comment These two spaces are not homeomorphic…right? @ForeverMozart: That comment essentially makes the connection between my answer and Henno’s. Mine is intended to be as elementary as possible. 13h answered These two spaces are not homeomorphic…right? 14h answered What is an order of an element of a partition"? 15h comment Is the space of subsets of $\mathbb R^n$ with the Hausdorff metric separable? The first term that I learned for a set like $N$ is $\epsilon$-net. 18h awarded Enlightened 18h awarded Nice Answer 1d answered Convergence of subnets