gesang reviewed General Topology by Stephen Willard
A relatively hard book
4 stars
A relatively hard book (well, general topology is not a hard subject) that I thought I won't need to read but turned out that is a must read. It is an absolutely comprehensive book on the subject of general topology. If you're gonna work with hard-core topology-oriented subjects such as C*-algebra, it'll be really helpful, since otherwise you'll certainly be perplexed by those strange jargons, such as upper-semicontinuous, lower-semicontinuous, weak topology, strong topology, etc. Even if you've read the book by Janich, etc., and read the three Rudin's.
One deficiency is that too many materials are in the exercises. I don't really think an undergraduate/beginning graduate have the time and the mathematical maturity to penetrate this book, since as far as I've seen they typically struggle with Rudin's functional analysis, which is easier. And for working mathematicians these results are old and tedious, unsuitable for working out by hand. We …
A relatively hard book (well, general topology is not a hard subject) that I thought I won't need to read but turned out that is a must read. It is an absolutely comprehensive book on the subject of general topology. If you're gonna work with hard-core topology-oriented subjects such as C*-algebra, it'll be really helpful, since otherwise you'll certainly be perplexed by those strange jargons, such as upper-semicontinuous, lower-semicontinuous, weak topology, strong topology, etc. Even if you've read the book by Janich, etc., and read the three Rudin's.
One deficiency is that too many materials are in the exercises. I don't really think an undergraduate/beginning graduate have the time and the mathematical maturity to penetrate this book, since as far as I've seen they typically struggle with Rudin's functional analysis, which is easier. And for working mathematicians these results are old and tedious, unsuitable for working out by hand. We need to know the history of the subject to get a grasp of the big picture, but these technical details are, for most of us, legacy, that are soon to be superseded by more abstract and succint notions.
The Historical Notes section is a gem, by the way.