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I is a proper subset Of K. Question 10. (Total 36pts) For the closed interval [0, 1], following the classical definition of the triplicate Cantor set C(3) discussed in the book and my class to define a new Cantor-type set C(5) through dropping the second and the fourth open subintervals at each generation. That is, given Co (5) := [0, 1], define C1 (5) = Co (5) \\ ( 3 ) UGS). C2 (5) := C1(5) \\ (25 25) U (25' 25) U (11 12) 25 ' 25 JU(3, 23) U ( 23, 23 ) U ( 23, 26) C (5): = no ci(5). Prove that Part A (5pts) Construct C3 (5) following the provided construction as above. Part B.(5pts) This new Cantor set C(5) has a (linear) measure zero by computation; that is, C(5) is of zero length. Part C.(6pts) This new Cantor set C(5) has the same cardinality as R; that is, C(5) is of continuum cardinality. Part D.(3pts) This new Cantor set C(5) is compact using the definition of compact set you learnt in class. Part E.(4pts) This new Cantor set C(5) is perfect; that is, C(5) has no isolated point. Part F (5pts) This new Cantor set C(5) is totally disconnected; that is, every pair of points of C(5) are disconnected. Part G (3pts) This new Cantor set C(5) is nowhere dense; that is, C(5) is composed entirely of discrete points. Part H. (5pts) The duplicate C(5) + C(5) of this new Cantor set C(5) covers the entire closed interval [0, 2]