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functional analysis - Where can I find the paper Un théorème de . . . J P Aubin, Un théorème de compacité, C R Acad Sc Paris, 256 (1963), pp 5042–5044 It seems this paper is the origin of the "famous" Aubin–Lions lemma This lemma is proved, for example, here and here, but I'd like to read the original work of Aubin However, all I got is only a brief review (from MathSciNet)
modular arithmetic - Prove that that $U(n)$ is an abelian group . . . Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
Mathematics Stack Exchange Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers
general topology - (Un-)oriented manifold with (un-)oriented interfaces . . . An un-oriented manifold is glued from pieces of oriented manifolds [with boundaries], separated by interfaces [where boundaries are glued]? I suppose a Mobius strip is one example, but do we have any concrete 4-dimensional example [glued from 3-dimensional interfaces] and 3-dimensional manifold examples [glued from 2-dimensional interfaces]?
(Un-)Countable union of open sets - Mathematics Stack Exchange $\begingroup$ A remark: regardless of whether it is true that an infinite union or intersection of open sets is open, when you have a property that holds for every finite collection of sets (in this case, the union or intersection of any finite collection of open sets is open) the validity of the property for an infinite collection doesn't follow from that
$U(n) \\simeq \\frac{SU(n) \\times U(1)}{\\mathbb{Z}_{n}}$ isomorphism Stack Exchange Network Stack Exchange network consists of 183 Q A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers