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Aug
11
revised when do norm-continuous unitary representations separate points of a group?
english grammar
Aug
11
comment when do norm-continuous unitary representations separate points of a group?
François, actually I'd like to have a theorem for general situation (not only for Lie groups, but a description for this subclass among all locally compact groups)... Is it possible that there is a gap between SIN-groups and those I am interested in?.. (Thank you for the reference anyway!)
Aug
11
revised when do norm-continuous unitary representations separate points of a group?
misprints
Aug
10
revised when do norm-continuous unitary representations separate points of a group?
I added "unitary" in the title
Aug
10
asked when do norm-continuous unitary representations separate points of a group?
Aug
5
comment A fixed point problem
Oh, I missed this.
Aug
5
comment A fixed point problem
@dimo Something is wrong, we do not understand each other. You consider a map from the closed interval $[0,1]$ into the plane $\mathbb R^2$ acting by formula $t\mapsto (tr,1-t)$ -- is this correct? And $A$ is the image of this map. If this is correct (and $[0,1]$ and $\mathbb R^2$ have usual topology), then this map is a homeomorphism between $[0,1]$ and $A$. (By the way, in this case it doesn't matter whether $r$ belongs to $\mathbb Q$ or to $\mathbb R$.)
Aug
5
comment A fixed point problem
Of course, this works only if I understand you correctly: the topology on $\mathbb R^2$ must be the usual topology of direct product of two $\mathbb R$, and each of those $\mathbb R$ is endowed with the usual topology of $\mathbb R$ (i.e. intervals $(a,b)$ form a base of open sets).
Aug
5
comment A fixed point problem
This is a general theorem: every bijective and continuous map from a compact space to a Hausdorff space is a homeomorphism, see R.Engelking, General topology, 3.1.13, see also Wikipedia en.wikipedia.org/wiki/Compact_space#cite_note-10 (the properties of Hausdorff spaces).
Aug
3
comment What are the qualities of a good (math) teacher?
I saw math teachers who are unable to build a logical chain carefully, without gaps and/or mistakes. I think, Jose had in mind that a teacher must have enough qualification for doing this in case when he sees that his pupils don't understand the logic of the exposition. Not that every time he must explain each millimeter of the proof. Am I right, Jose? :)
Jul
31
comment A single paper everyone should read?
I wonder if there is a progress since that time in the directions that Dyson mentioned as what should be done.
Jul
29
comment A fixed point problem
I don't understand the problem. $A$ is homeomorphic to the interval $[0,1]$. So everything follows from the Brouwer fixed-point theorem (it's variant for the dimension 1). The statement of the problem looks strange.
Jul
21
awarded  Revival
Jul
21
answered Hahn-Banach restricted to a pre-dual
Jul
21
accepted “Uniformly (co)well-powered” categories?
Jul
21
comment “Uniformly (co)well-powered” categories?
Andreas, which reading do you recommend?
Jul
20
revised “Uniformly (co)well-powered” categories?
deleted 466 characters in body
Jul
20
comment “Uniformly (co)well-powered” categories?
Yes, I found this result about well-ordering of the class of all sets in A.Levy's book. Andreas, I think you should put what you wrote in form of answer, and I will close this question. I'll make corrections in the question so that your answer will be natural. Or I do not know what to do with this. Eric, I still do not understand what you wrote. That is interesting, please, give me a reference.
Jul
20
comment “Uniformly (co)well-powered” categories?
@Eric and Andreas, I need a reference. This is the first time I hear this. The class of all sets can be well-ordered? And this trick with sending X to the set of all skeleta... Is there a text to look how people do this?
Jul
20
comment “Uniformly (co)well-powered” categories?
To apply the axiom of choice (i.e. to choose this map $X\mapsto S_X$) we must already have a map which to every $X$ assigns a set which contains some $S$ as element. But we do not have such a map. Or you mean something else?