Are Kuratowski's topology textbooks good?

Question

I'm looking for a good book to teach myself topology, and I already know a little bit of topology.

Answer 1

They contain an enormous amount of material, far more than any usual textbook, but I cannot recommend them for your purpose: they make far better reference works than textbooks. They contain too much information to be a good textbook, especially for self-learning the subject, and the style of presentation is very compact. Moreover, some of the notation is quite different from current usage. For instance, instead of $\{x:\varphi(x)\}$, Kuratowski uses the obsolete notation

$$\underset{x}{\large{E}}\varphi(x)\;.$$

Similarly, if $F(t)$ is a subset of $X$ for each $t\in T$, he writes

$$\underset{t\in T}{\large{P}}F(t)$$

for $\prod_{t\in T}F(t)$. These may seem like small things, but they add up, and the first is especially problematic.

If you already have the basics and some mathematical sophistication, you might be in a position to use Stephen Willard’s General Topology, which remains one of the best texts at the advanced undergraduate/beginning graduate level. He leaves a lot to the exercises, but he also offers quite a few hints in those exercises.