推 znmkhxrw :因為f^-1把R中的任意closed打到closed 10/30 00:42
→ znmkhxrw :所以by thm, (f^-1)^-1 is continuous 10/30 00:42
→ znmkhxrw :就是f is continuous 10/30 00:42
→ znmkhxrw :阿~~你的f^-1是函數嗎？？ 如果只是pull back.... 10/30 00:43
→ znmkhxrw :我在講什麼= =" 重來....XD 10/30 00:45
→ znmkhxrw :f is continuous at A iff for all closed subsets 10/30 00:46
→ znmkhxrw :of f(A), denoted by B ,f^-1(B) is relative closed 10/30 00:47
→ znmkhxrw :at A 10/30 00:47
推 znmkhxrw :所以如果你的f(R)=R(onto) f 應該會是continuous 10/30 00:49
→ znmkhxrw :如果f(R)不等於R 那你的H要跟f(R)取交集 10/30 00:51
→ znmkhxrw :不然會超出定義範圍 10/30 00:51