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Munkres text question.

  1. Aug 8, 2011 #1
    I cant seem to find a answer for 20.7 anywhere. Unfourtantly, I do not have the skills to latex the problem out, so I only hope someone looks in the book.

    My solution is that the supremum of the set of a_i 's must be finite above and the infinium is finite and greater then zero , and the b_i 's have no restraints.
  2. jcsd
  3. Aug 8, 2011 #2
    Hi Fisicks! :smile:

    What is that an answer to?? To the continuity of h or to h being a homeomorphism.

    For h to be continuous, you are correct: we only need to demand that [itex]\sup{a_i}<+\infty[/itex].

    But for h to be homeomorphism, it is also correct, we demand that [itex]\sup{a_i}<+\infty[/itex] and [itex]\inf{a_i}>0[/itex].

    Note, the map in this exercise is often called a "diagonal operator". So you can search it by that name :smile:
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