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安裝中文字典英文字典辭典工具!
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- (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
- Show that - 1 2(4 - Un)$ - Mathematics Stack Exchange
We know (from a previous question) that Un is an increasing sequence and Un < $4$ Show that $4$ - Un+1 <(or =) 1 2(4-Un) I gave it a try and this is what I got :
- Mathematics Stack Exchange
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- 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]?
- Mnemonic for Integration by Parts formula? - Mathematics Stack Exchange
The Integration by Parts formula may be stated as: $$\\int uv' = uv - \\int u'v $$ I wonder if anyone has a clever mnemonic for the above formula What I often do is to derive it from the Product R
- Intuitive proof that $U(n)$ isnt isomorphic to $SU(n) \\times S^1$
This is a sort of addendum to Qiaochu's answer, the purpose of which is to tie up the loose end it leaves in the sense that it only considers isomorphisms compatible with the short exact sequence associated to the surjective $\det\colon \mathrm{U}(n) \to S^1$
- modular arithmetic - Prove that that $U(n)$ is an abelian group . . .
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- $U(n) \\simeq \\frac{SU(n) \\times U(1)}{\\mathbb{Z}_{n}}$ isomorphism
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