## Sunday, September 21, 2008

### I Have Wireless

So I have finally managed to get my wireless card working with Ubuntu 8.04. You have no idea how happy I am about this. I have been wanting to really give Ubuntu a try but have always been reluctant to because of the fact that it wouldn't work with my wireless card and I would need an ethernet cable in order to connect to the internet. Now I know this happiness will not be too long lived because once I update to the next version of Ubuntu (which in my case will probably be 9.04 and not 8.10) I will most likely have to go through the same process again and hope that it still works on the new version.

On a more "depressing" note; I managed to finish only half of one my my 5 analysis homework problems. They all seem to be about connected sets. One of the funny things is that in Rundin for a set to be connected it must not be able to be written as the union of two separated sets. However, on Wikipedia, Mathworl, and one of my other analysis text they also say that the separated sets must be open sets. Now I know that if two open sets are disjoint they are separated so I don't see the real need for this extra assumption. In any case the problem I managed to solve was as follows.

Let A and B be two connected subsets of a metric space X. Show that is A and B have nonempty intersection then their union is also connected.

The second half of the problem asked us to state and prove a generalized version of this for the union of arbitrary connected sets. I came up with:

Let {A} be collection of connected sets. If for each F in {A} there exist a G in {A} such that the intersection of F and G is nonempty then the union of all the members of {A} is a connected set.