![arXiv:math/9911224v2 [math.GT] 9 Dec 1999](http://s1.studyres.com/store/data/016370695_1-31d422643fefeca7faefc96120ceb1d7-300x300.png)
Practice Test, Topology, Autumn 2011 Question 1 Question 2
... Solution: A set is open if it is either empty or it its complement is finite. (ii) Prove that the finite complement topology is, in fact, a topology. [4 marks] Solution: Given a set X, the finite complement topology is τ = {U ⊂ X : X \ U if finite, or U = ∅}. By definition, ∅ ∈ τ , and X ∈ τ because ...
... Solution: A set is open if it is either empty or it its complement is finite. (ii) Prove that the finite complement topology is, in fact, a topology. [4 marks] Solution: Given a set X, the finite complement topology is τ = {U ⊂ X : X \ U if finite, or U = ∅}. By definition, ∅ ∈ τ , and X ∈ τ because ...
Some Notes on Compact Lie Groups
... have x · y = y · x and |x|2 = xx = xx = 4i=1 (xi )2 . In particular, a non-zero element x has the inverse x/|x|2 . Thus H is a field. It has R = {x1 } and C = {x1 + ix2 } as subfields. Note that Hn can be regarded as a complex vector space, where the scalar multiplication is the multiplication from ...
... have x · y = y · x and |x|2 = xx = xx = 4i=1 (xi )2 . In particular, a non-zero element x has the inverse x/|x|2 . Thus H is a field. It has R = {x1 } and C = {x1 + ix2 } as subfields. Note that Hn can be regarded as a complex vector space, where the scalar multiplication is the multiplication from ...
Lecture 8 - Universal Enveloping Algebras and Related Concepts, II
... by π T (l). Further, U (g) is naturally a U (l)-module in the algebra sense. ...
... by π T (l). Further, U (g) is naturally a U (l)-module in the algebra sense. ...
