Hew Wolff
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 Mar 27 awarded Self-Learner Oct 6 awarded Nice Question Oct 6 asked Is “polynomials in $x$” a monad? Jun 23 awarded Yearling Jun 14 awarded Tumbleweed Jun 7 asked free algebras over noncommutative rings May 24 comment Generator of group $D_n$ Try this: pick one side of the polygon, and think about where a symmetry could take that side. I think that will tell you that the symmetry is either a rotation or a rotation with a reflection. May 24 answered Extreme value theorem, without Heine Borel. May 24 comment Try to use Homogeous space Characterize the space of all lines in the plane . Presumably you prefer to find a smooth structure which is compatible with some other information such as the symmetries of the plane. Otherwise, you could simply observe that the set of straight lines can be put in one-to-one correspondence with the real numbers, and then use the smooth manifold structure on $\mathbb{R}$. May 24 comment Try to use Homogeous space Characterize the space of all lines in the plane . It looks like Theorem 21.20 gives your result directly; you don't need to know anything about $G / G_m$. What do you feel is missing from that argument? May 13 comment Questions about homomorphisms? "But why are the kernels ideals": people thinking about rings realized that ideals are important, and that kernels are important, and that these are basically the same thing. May 13 answered Questions about homomorphisms? May 7 answered Comparing Open Bases and Covers May 7 comment Finite abelian groups of order 100 Hint: what's the order of the group $Z_2 \times Z_5$? That order depends on $2$ and $5$ in a simple way. May 6 comment Preserving compactness and connectedness implies continuity for functions between locally connected, locally compact spaces? I think you have to admit that between me and @BrianMScott, your original question is now answered... May 1 answered Preserving compactness and connectedness implies continuity for functions between locally connected, locally compact spaces? Apr 28 comment Suppose $A$ is a nonempty subset of $\mathbb{R}^n$. Prove that if $A$ is both open and closed, then A=Rn. There's no obvious notion of "bounded above" or "sup" in $\mathbb{R}^2$. However, @BolzWeir's argument is good if you know that $\mathbb{R}$ is connected and that products preserve connectedness. Apr 28 comment Proving that two equivalence classes are disjoint? Yes, that's right. Now you have to show that $1 R a$ and $0 R a$ can't both be true. Apr 28 comment Proving that two equivalence classes are disjoint? $0^{\overline{0}}$ does not appear to mean anything; just say $\overline{0}$ and $\overline{1}$. Apr 21 comment How to scale a random integer in $[A,B]$ and produce a random integer in $[C,D]$ I added some details, see if that helps.