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第25講 5.5 The space of Continuous Functions(cont.)

L25_A
        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.)
              (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.)
              (1)Thm:complete in normed space
              (2)Rmk:While both Cb(A,N) and R^n are normed
                  spaces,they are quite different 
              (3)Definition of Banach space and Hilbert space
  
L25_D
        5.5 The space of Continuous Functions(cont.)
              (1)example:E is open in C([0,1],R)

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