Exercise 1. Find metric topological spaces [tex]A,B,C[/tex] such that [tex]A[/tex] is **not** homeomorphic to [tex]B[/tex], but [tex]A\times C[/tex] **is** homeomorphic to [tex]B\times C[/tex].

Exercise 2. Find **path connected** metric topological spaces [tex]A,B,C[/tex] such that [tex]A[/tex] is **not** homeomorphic to [tex]B[/tex], but [tex]A\times C[/tex] **is** homeomorphic to [tex]B\times C[/tex].