bio | website | math.wustl.edu/~nweaver |
---|---|---|
location | ||
age | ||
visits | member for | 3 years, 4 months |
seen | 1 hour ago | |
stats | profile views | 5,972 |
Aug
23 |
comment |
May open sentences be eliminated?
Naslazhdaites Peterburg. Udacha! |
Aug
22 |
comment |
May open sentences be eliminated?
I'm not sure why you think that, but again, look at the book by Troelstra and van Dalen. What I am telling you is a general fact of logic. Extensionality is only meaningful in set-theoretic settings and doesn't come into it. |
Aug
22 |
comment |
May open sentences be eliminated?
Look at the reference I gave. $(\forall x)A(x) \to A(t)$, with $t$ free for $x$ in $A$, is one of the Hilbert axiom schemes. No, you don't need set abstracts, this works for any first order predicate calculus with only the modifications I stated. |
Aug
21 |
answered | May open sentences be eliminated? |
Aug
19 |
reviewed | Approve Explicit formula for Riemann zeros counting function |
Aug
18 |
comment |
Stone-Cech compactification of $\mathbb{R}^n$ and smooth functions
Why don't you ask the professor? No doubt they had a definite reason for proving this result and would be happy to explain it. |
Aug
17 |
reviewed | Approve Projective & injective dimensions |
Aug
17 |
comment |
Corresponding between prime ideals in $C(X)$ and $C^*(X)$
If you want people to help you out by doing some work to solve your problem, you're going to have to explain your notation better. I clicked your link but I'm not going to hunt through an entire book to find definitions of notation that you could easily supply in your question. |
Aug
17 |
reviewed | Approve Characterization of Fréchet-Urysohn spaces using sequential continuity at a point |
Aug
17 |
reviewed | Approve Subfields of $\mathbb{C}$ isomorphic to $\mathbb{R}$ that have Baire property, without Choice |
Aug
15 |
reviewed | Reject Example of 4-manifold with $\pi_1=\mathbb Q$ |
Aug
15 |
comment |
Formula for the distance in noncommutative geometry
Oh, you're right! Still maybe not so hard to fix, but I withdraw the criticism. |
Aug
15 |
comment |
Formula for the distance in noncommutative geometry
No problem. You don't really need to cite a reference for this construction; just compose the distance function with some $C^\infty$ function $g: [0,\infty) \to [0,\infty)$ satisfying $g(t) = 0$ on $[0,\epsilon/2]$, $g(t) = t - \epsilon$ on $[\epsilon,\infty)$, and something reasonable on $(\epsilon/2,\epsilon)$. |
Aug
15 |
comment |
Formula for the distance in noncommutative geometry
So the answer to question 1 is "yes". |
Aug
15 |
comment |
Formula for the distance in noncommutative geometry
You're right that the closure of $C^\infty(M)$ in Lipschitz norm is $C^1(M)$, but that is enough to attain the distance formula. The distance-from-$p$ function $d(p,\cdot)$ is already $C^\infty$ everywhere except at $p$. You can just smooth it out near $p$ and get a function that is $C^\infty$, has Lipschitz number 1, and separates $p$ and any other point $q$ by at least $d(p,q)-\epsilon$, for arbitrary $\epsilon$. |
Aug
14 |
reviewed | Reject Reference request: Strong Connectivity and the Incidence Matrix |
Aug
13 |
comment |
$C^{*}$ algebras which do not admit nontrivial idempotent morphism
Your example 2 is just a special case of the general phenomenon of topological retracts (noted by Ali Taghavi in his comment to my answer). |
Aug
12 |
answered | $C^{*}$ algebras which do not admit nontrivial idempotent morphism |
Aug
11 |
awarded | Self-Learner |
Aug
11 |
accepted | Separating pure states on the $2\times 2$ matrix algebra |