Mistakes Were Made

I knew - I knew - it wasn't going to work.

The forecast for today is for "scattered storms". I saw this in action shortly after getting up, when I had to race outside (clad in bathrobe, carrying umbrella) to retrieve the paper from a pummelling rainshower.

For timing reasons, I wasn't able to walk the dogs yesterday, so I felt obligated to do so today. Looking outside, I saw that, though the cloud cover was heavy and dark, it wasn't raining, so I leashed up the dogs and headed out.

As we walked, I allowed the dogs to stop and sniff, but admonished them against their efforts to backtrack and catch something they'd missed. Fortunately, we hadn't gone too far when the skies opened up, so turning around (and contradicting my own admonitions) was feasible. The rain was a heavy fall of big fat drops, so I started running. Buster kept up easily, but after a few strides Gracie was lagging (and in fact resisting), so I paused to scoop her up. (Buster took the opportunity to, rather uselessly, shake.)

We were not completely soaked; I've had to take off my shirt, but no more than that. Gracie looks distinctly wet-rattish, but she's not (now) wet, just disheveled. Buster got up on the bed and rolled, but doesn't seem to have gotten the sheets too wet.

Oh, yes. We're out of dog food. It's not raining right at the moment....

Facebook

Some months ago, I received an e-mail, informing me that :name: (a former student of mine) had joined Facebook and inviting me to do likewise. I have been reluctant to respond to the message, but it has been followed by two repetitions, at intervals of a month or so. I have a couple of questions, then, for anyone who might be more familiar with Facebook than I am.

First, and to me most important: it seems clear that the messages are, in some sense, automatically generated. (They address me as "Dear Dr.", for instance.) Question: does the new Facebook member choose who is to receive such messages, or does Facebook simply raid the address book?

Second, for those who are or have been on Facebook: what are the benefits, and what are the detriments, of joining?

Any information would be gratefully received.

A Taste of Topology

As I've mentioned before, this summer I'm teaching a course in topology. One of the pleasures of teaching a new course, especially an advanced one, is re-encountering material you (in theory) learned many years ago, but seeing it with a more mature and experienced eye. Last week, we covered "Urysohn's Lemma", and I found to my delight that its proof (long since submerged) is, well, really neat.

I'm going to spend a post or three laying out enough background that I can give the basic structure of the proof, without going into all the grungy details. Look under the cut... if you dare....

( Point-set Topology )