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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