L25_A
5.5 The space of Continuous Functions(cont.)
5.5 The space of Continuous Functions(cont.)
(1)Property:function in a normed space
(2)Remark
(3)Thm: Cb(A,N) in metric space & normed space
L25_B
5.5 The space of Continuous Functions(cont.)
5.5 The space of Continuous Functions(cont.)
(1)Questions: What does D(f,r) look like?
(2)In Cb(A,N),what kinds of subset is
open,closed,compact,connected?
(3)Thm
L25_C
5.5 The space of Continuous Functions(cont.)
5.5 The space of Continuous Functions(cont.)
(1)Thm:complete in normed space
(2)Rmk:While both Cb(A,N) and R^n are normed
spaces,they are quite different
spaces,they are quite different
(3)Definition of Banach space and Hilbert space
L25_D
5.5 The space of Continuous Functions(cont.)
5.5 The space of Continuous Functions(cont.)
(1)example:E is open in C([0,1],R)
10610高等微積分練習題_1(暫).jpg
