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location Berkeley, CA
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seen 23 mins ago

I'm a second-year graduate student in pure mathematics at UC Berkeley. You can contact me at qchu[at]math[dot]berkeley[dot]edu.


15h
comment cohomology is dual to homology of a spectrum if homology is free
I think the point is that $E^X$ is also the spectrum of morphisms $E \otimes \Sigma^{\infty} X_{+} \to E$ of $E$-modules, but I could be wrong.
17h
comment Find a subgroup of $S_4$ that is isomorphic to V, the Klein group.
It's the same $4$ as in $S_4$; in particular it makes the list of transitive subgroups of $S_4$ look more uniform. $C_4, V_4, D_4, A_4, S_4$.
17h
comment Find a subgroup of $S_4$ that is isomorphic to V, the Klein group.
The Klein group acts by left multiplication on itself.
18h
comment Presheaf of real valued functions
That is not what it does. It associates the set of all continuous functions $f : U \to \mathbb{R}$ to each open set $U$.
23h
revised The semidirect product as a deformation of the direct product
added 66 characters in body
23h
answered The semidirect product as a deformation of the direct product
23h
comment surjection between sets which are defined through a functor
What? But you have no guarantee that $T(\pi_X)$ is invertible.
1d
comment The semidirect product as a deformation of the direct product
I think this is the wrong way to think about the semidirect product. In fact the semidirect product is not a product at all. See math.stackexchange.com/questions/867203/….
1d
comment On loop space of a product
I don't really see the point of this question. The moment it occurs to you to talk about loop spaces this is one of the first things you could prove about them, and it doesn't particularly take any ingenuity to do so.
1d
comment More elegant proof of that this diagram commutes
The point is that you've written down a functor called "forgetting the complex structure." If you ask yourself how to state this theorem without using coordinates then there is practically nothing to prove.
1d
comment $A\oplus C \cong B \oplus C$. Is $A \cong B$ when $C$ is finite, A and B infinite.
If by $\oplus$ you mean direct product, this is true at least if $A, B$ are also finite; see groupprops.subwiki.org/wiki/….
1d
comment Isomorphism between two magmas with one.
This is already an undecidable problem for groups.
1d
comment Is there a name for a property defined in terms of open sets?
I think that is not quite what the OP is asking, although I could be wrong. For example, "cardinality of the underlying set" is a topological invariant which is not defined in terms of open sets. Properties of topological spaces defined only in terms of their open sets are properties of their underlying locales (en.wikipedia.org/wiki/Pointless_topology), so really should be called localic properties, I guess.
1d
awarded  Nice Answer
1d
comment Orthonormal basis for a tangent plane
Have you considered any examples?
1d
comment Curve avoiding semi-rational points
Surely not. By hypothesis the projection of the curve to some coordinate is nonconstant, so its image necessarily contains a rational.
1d
comment Orthonormal basis for a tangent plane
Once you have any basis at all, you can apply Gram-Schmidt to it to get an orthonormal basis.
1d
comment What are the non-trivial normal subgroups of $O(3)$?
You're doing too much work. $SO(3)$ is the kernel of the determinant, which is a group homomorphism, and the kernel of a group homomorphism is always a normal subgroup.
1d
comment surjection between sets which are defined through a functor
For example, the functor $T(X) = X \times S$ for a fixed set $S$ does not have this property as long as $S$ has at least two elements.
1d
comment What are the non-trivial normal subgroups of $O(3)$?
Indeed the complement of $\text{SO}(3)$ is not a subgroup: it's not closed under multiplication and it doesn't contain the identity.