Introduction to Mathematical Analysis I - Second Edition

61 2.6.4 Prove that the intersection of any collection of compact subsets of R is compact. 2.6.5 Find all limit points and all isolated points of each of the following sets: (a) A = ( 0 , 1 ) . (b) B = [ 0 , 1 ) . (c) C = Q . (d) D = { m + 1 / n : m , n ∈ N } . 2.6.6 Let D = [ 0 , ∞ ) . Classify each subset of D below as open in D , closed in D , neither or both. Justify your answers. (a) A = ( 0 , 1 ) . (b) B = N . (c) C = Q ∩ D . (d) D = ( − 1 , 1 ] . (e) E = ( − 2 , ∞ ) .