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visits member for 2 years, 5 months
seen 6 hours ago

I'm a PhD student at UCLA.


6h
comment Why do we care about non-$T_0$ spaces?
Most of the questions you might ask on pointless topology would fit under either order theory/lattice theory or topos theory. Regarding the main question, I don't know an important use for non-$T_0$ spaces. There are very important non-$T_1$ spaces, namely, spectra, so the distinction is either sharp or wrong.
18h
comment The name for the quotient property.
Well, agreed that it's easy to construct such a map, but that example doesn't look obviously natural to me. Maybe it comes up in functional analysis or something when one works at several levels of the lattice of topologies simultaneously? Anyway, that's to one side.
18h
comment Drawing toral automorphisms
You translate by whole integer jumps along one or the other axis, and observe that there's exactly one suchjump that gets each piece into the standard unit square. Alternatively, take the decimal part of each coordinate of each point in each piece.
1d
comment The name for the quotient property.
Ah, sorry, I didn't catch that you wanted a name for a not-necessarily continuous map that satisfies the second property. I agree that there's probably not a name for it in itself, because there are probably no natural examples of such maps that aren't continuous.
1d
answered The name for the quotient property.
1d
answered Drawing toral automorphisms
1d
answered Question about convergence in complex numbers field
1d
revised Question about convergence in complex numbers field
deleted 2 characters in body
2d
comment Proof explanation Mayer-Vietoris and the Punctured Euclidean Space.
You're being too picky. There is a discrepancy, but it's not significant.
2d
comment Proof explanation Mayer-Vietoris and the Punctured Euclidean Space.
Well, the question statement gives the correct cohomology groups for $n\geq 2$, which is what it says it's going to do. And the author gives the correct group for $n=1$.
2d
comment Basis and dimension of the null space and range
Can you think of any elements of $\mathbb{R}^{n\times n}$ that are in the null space? Once you see what it means to be in the nullspace, the problem becomes simpler. For the other part, the trick is, similarly, to figure out: what interesting property do all elements of the range have?
2d
answered Proof explanation Mayer-Vietoris and the Punctured Euclidean Space.
2d
answered Layman's Question on Schemes
Oct
19
comment Techniques to prove a function is uniformly continuous
The first step in such a question is to search this site! See the link. Also, you need to use the other kind of slash for your deltas and epsilons. math.stackexchange.com/questions/503093/…
Oct
19
comment Techniques to prove a function is uniformly continuous
Regarding formatting, there's nothing to learn: you literally just need to enclose your math in dollar signs and add backslashes before character sequences like epsilon, delta, and sqrt.
Oct
19
answered Techniques to prove a function is uniformly continuous
Oct
18
comment Yoneda Lemma: definition of Yoneda functors
No, it's $\mathcal C^\vee$ and $[\mathcal C,\mathbf{Set}]$ that are opposite: what you said is the common mistake I mention in my first paragraph. If you think of some examples you'll see there's no way to get a contravariant functor from a covariant one in general.
Oct
18
answered A base of topology
Oct
18
answered Is the null space inside the collumn space of a matrix?
Oct
18
comment Can the scalars of a vector space be of a different field than the entries of the vector space?
Yes, they are, so the real numbers can naturally be the scalars for any complex vector space. I'm saying in some cases you can actually extend the scalars in the other direction. But this isn't an important point-feel free to ignore it.