7,997 reputation
1624
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location Cambridge, UK
age 23
visits member for 2 years, 3 months
seen 2 hours ago

I'm a PhD student at UCLA.


Aug
24
comment Why does every noncompact orientable surface have a complex structure?
The punctured torus doesn't embed because that would extend to an embedding of the torus, since every circle in the plane bounds a disk. Similarly an embedding of the surface of countable genus would restrict to an embedding of the punctured torus. @Troy Woo Huybrechts has the best book on complex manifolds.
Aug
24
answered Why does every noncompact orientable surface have a complex structure?
Aug
23
answered Is there a natural (non-trivial) topology for the automorphism group of a locally compact abelian group?
Aug
19
comment Has the opposite category exactly the same morphisms as the original?
Yes, that's correct.
Aug
19
answered Has the opposite category exactly the same morphisms as the original?
Aug
19
comment Homotopy direct limit versus direct limit
This is in the category of topological spaces, probably the algebraic topologists' category to be precise, so something like compactly generated spaces with nondegenerate basepoint.
Aug
18
accepted Nonstandard complex numbers and categoricity
Aug
18
comment Cohomology of wedge equals direct sum of cohomologies
Surely it's not the coproduct you want here, but the product? Just thinking of the wedge of two circles over $\mathbb{Z}$, where the free product would have elements of infinite order with respect to the cup product.
Aug
18
comment Nonstandard complex numbers and categoricity
Thanks to both of you. I had been counting real algebra automorphisms, rather than field automorphisms, of $\mathbb{C}$, so that helps me believe in stranger isomorphisms such as this one. If I can try to explain my current understanding: the answer to my question is "yes," but my discussion of lines is wrong because the absolute value on ${}^*\mathbb{C}$ will be realized in $\mathbb{C}$ in terms of some wild embedding of $\mathbb{R}$. If that's still off base, I'd appreciate more elaboration from either of you.
Aug
17
comment Homology and topological propeties
There's a lot of notation in there. What are the $(C)_{c'}$ condition, $K^c_\phi,H_k, M_k,\beta_k$?
Aug
17
asked Nonstandard complex numbers and categoricity
Aug
14
comment Does $2+2$ really equal $4$?
While this is a good answer in itself, I think it's probably incomprehensible to the OP, who in particular may not know the words "isomorphism," "second order," or "recursion" or be able to read explanations of what a free monounary algebra is.
Jul
30
comment Ever thought of differentiate brackets for function and for order of operations?
You could do this in your own work, but it would be more trouble than it was worth to change widely.
Jul
29
answered Relation between continuous maps and convergence of sequences
Jul
22
awarded  Pundit
Jul
7
comment Parametrizing Walks on Sphere and Torus
That's amazing indeed-I'm glad you saw this.
Jul
6
comment Possible Fields?
You can put the discrete metric on any field you like to get a complete metric space, but otherwise the answer is no-any complete metric space is either uncountable or has isolated points, so if you want your metric to be translation invariant a topological field is either uncountable or discrete.
Jul
2
awarded  Curious
Jun
30
answered Definition of forgetful functor
Jun
29
comment Proving result on measure's atoms
We may assume the sum is of numbers less than or equal to 1 by normalizing, since of course an unbounded sum diverges. Decompose such a sum into subsums of numbers between $1/n$ and $1/n+1$. One of these subsums must be infinite, indeed uncountable, since otherwise the entire sum decomposes as a countable collection of countably many numbers.