Topological Notation

In general topology, one talks about open and closed sets a lot. A lot. So it seems a bit silly that there isn’t standard notation for that; it’s sort of like writing “equals” longhand throughout and entire semester of calculus. So I came up with the following simple symbols:

• ( is open in );
• ( is closed in );
• (the interior of A);
• (the closure of A).

They’ve been saving me a lot of time and thought since then, like notation’s supposed to. Witness . The closure symbol, in particular, has ended the ambiguity with , which often denotes the complement of in other contexts. It’s easy to know which is meant if you think about it, but this sort of thing should be run by the cerebellum.

Shame on you, Amazon

I have long been an eager customer at Amazon.com. Their collection is damn impressive, and their website is, imho, tied with Wikipedia for best on the Internet (discounting meta-sites like Google). Ever since “Search inside this book” and the revamping of the recommendations interface/algorithm, I find myself spending more time on it than on almost any other single website.