Exercises on Homeomorphisms and Connectedness

  1. Which of the following are homeomorphic? (Informally justify why or why not based on arguments related to content we covered in class)
  2. Prove why each of the following is or is not connected: Rl and Rzar=Rfc

  3. Use ideas of connectedness to informally show that no pair of the following is homeomorphic: (0,1), (0,1], [0,1]