luch commented on Topology by Klaus Jänich
Thus far, i've found this an engaging read. The presentation of the material is lean, which has its advantages and disadvantages. I'm mostly reading this text as a review, so its complete lack of formal exercises and its brisk (but, crucially, complete) summary of undergraduate topology is perfect for me. But i think even the novice would find this an excellent companion to something like Munkres, the traditional introductory topology text. Indeed, this text presents a number of examples very clearly, with excellent diagrams and accompanying descriptions. Further, Jänich has a real talent for keeping the reader's eyes on the larger picture, on developing ideas and intuition, and not getting overly bogged down in technical details (which they trust the reader will be able to provide—these tend to serve as the text's exercises).
Perhaps the main thing to bear in mind while reading is that some portions of the text assume a knowledge of some background material that i would think would be unfamiliar to many, if not most, undergraduates. But… i've just been skipping things i've not been exposed to, or that i have only vague memories of. Doing so does not seem to disrupt the overall flow of the text; it merely leaves one with fewer examples to draw from, which is perfectly all right. It also gives one material to return to.
The point is: i like it very much, so far, about three chapters in.