# Munkres text question.

1. Aug 8, 2011

### Fisicks

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. Aug 8, 2011

### micromass

Staff Emeritus
Hi Fisicks!

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 $\sup{a_i}<+\infty$.

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

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