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1d
comment Is $\mathcal{P}(\omega)/fin$ with the interval topology path-connected?
Oh, I misread the definition, sorry.
1d
comment Is $\mathcal{P}(\omega)/fin$ with the interval topology path-connected?
According to your definition of "interval topology", it looks as though every subbasic open set is also closed, in any poset ...
Mar
23
awarded  Nice Answer
Mar
23
comment What are the applications of operator algebras to other areas?
@YemonChoi: +10 for "Atiyah is a dense point in mathematics"
Mar
23
comment What are the applications of operator algebras to other areas?
Huh. No, I haven't encountered this. But no doubt negativity towards other fields is fairly common --- I can be guilty of this myself --- though I suppose I feel it's something one shouldn't take too seriously. That's just human nature.
Mar
23
comment Obtain any 3-manifold from repeating surgeries on knots in $S^3$
Yes, this was my father.
Mar
23
answered Obtain any 3-manifold from repeating surgeries on knots in $S^3$
Mar
22
awarded  Explainer
Mar
22
answered What are the applications of operator algebras to other areas?
Mar
22
comment What are the applications of operator algebras to other areas?
@PaulSiegel: partly ... I just looked up the citation and it includes "applications of the theory of C*-algebras to foliations and differential geometry in general". A version of his index theorem appears in his paper "A survey of foliations and operator algebras" which is based on a talk given in 1980.
Mar
22
revised What are the applications of operator algebras to other areas?
deleted 122 characters in body; edited title
Mar
22
comment What are the applications of operator algebras to other areas?
@Vincent: Probably the part about "I've heard some things about the reputation of this area" and the placement of "operator algebras" in quotes gave this question a very different tone. I will edit the question to give it a more neutral tone.
Mar
22
comment What are the applications of operator algebras to other areas?
We have two Fields medals: Jones (connections between von Neumann algebras, physics, and knot theory) and Connes (a generalization of the Atiyah-Singer index theorem to foliated manifolds). Other obvious answers that spring to mind are applications to group representations and quantum statistical physics. If the question is reopened I will add this as an answer.
Mar
19
comment Lipschitz-free spaces of $\mathbb R^n$
I didn't know this.
Mar
8
awarded  Enlightened
Mar
8
awarded  Nice Answer
Feb
16
comment Connes' correspondences of two $L^\infty$-algebras
The result is not obtained for pairwise disjoint rectangles, it is obtained for sequences $\{A_n\}$ and $\{B_k\}$ each of which is pairwise disjoint.
Feb
15
comment Connes' correspondences of two $L^\infty$-algebras
I really don't think this proof is right. The result about $\gamma(\bigcup A_n \times B_n)$ is only proven when the sequences $\{A_n\}$ and $\{B_k\}$ are pairwise disjoint.
Feb
14
comment Connes' correspondences of two $L^\infty$-algebras
I don't follow the last part of the argument --- where does the decomposition $D_n = \bigcup_{i=1}^{M_n} D_{n,i}$ come from? But it seems to me that the usual proof of this lemma for product measures, where you integrate characteristic functions, should work.
Feb
13
answered strong convergence in Hilbert c* module