Malmo is rather quiet, so this building is one of the highlights. It is really just a tall apartment complex in a fantastic design. They don't allow any tourists into the building :(
If you have the time to explore the Church of Our Savior (very close by) you should do so. The walkway to the top of the spire is located on the outside of the church and can be climbed all the way. You can return to downtown Copenhagen by simply reversing the trip over.
250 steps on the inside, and 150 steps on the outside, and you are at the top of the church spire, from where you have the most magnificent view. Built 1749-52 and mentioned in Jules Verne's Journey to the Center of the Earth.
The Little Mermaid
One of the most famous tourist attractions in Copenhagen