1. Manetti 6.8

  2. Manetti 6.9

  3. Manetti 6.11

  4. Manetti 6.12

  5. Show that if \(X\) is a first-countable topological space and \((a_n)\) is a sequence from \(X\) and \(a\) is a limit point of \((a_n)\) then a subsequence \((a_{n_i})$ of\)(a_n)\(converges to\)a$$.