推 Lindemann :我知道這是定義,但是為何圓盤映到R^2是 f(x,y)???? 08/25 15:09
※ 引述《Lindemann (一個人最大的敵人是自己)》之銘言：
: 問一下Geometry,Topology and Physics second edition by Mikio Nakahara
: Nakahara(後來才知道叫做 中原三木雄)
: ㄧ個半徑為1的open disc映射到R^2的homeomorphism 同胚映射為
: 2 2
: f: D ---> R
: x y
: f(x,y)= (_____________ ________________ )
: 1/2 , 1/2
: [1-x^2-y^2] [1-x^2-y^2]
: -1 2 2
: 其中 f : R ---> D
: -1 x y
: f (x,y)= (_____________ ________________ )
: 1/2 , 1/2
: [1+x^2+y^2] [1+x^2+y^2]
: -1
: 上面的f (x,y)我有算出來,但是我就是不懂為何這樣子是
: open disc映射到R^2的homeomorphism,f到底是怎麼看呢???
note that a continuous mapping f:M->N which has continuous inverse mapping
f^-1:N->M is homeomorphism
obviously, f is homeomorphism
Rmk: every diffeomorphism is a homeomorphism
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 123.193.144.41