Basic Topology

Description

In my schooling for math, I have yet to encounter a worse text book than Armstrong. To begin with, the book opens with a long chapter that tries to motivate the subject by summarizing the rest of the book. Obviously this doesn't work out too well, as the reader has yet to even get a feel for topology; a lot of hand waving is utilized, and totally non-rigorous pseudo-definitions are given for important things, such as topological spaces themselves, that only serve to confuse later on. Then the author has the audacity to refer back to this chapter full of non-information when actually attempting to develop topology in a mathematically rigorous manner. As for organization, there is none. The book buries theorems and proofs in paragraphs. There are no signals that proofs are over, and one normally has to search the chapters for relevant information. It is also worth noting that said information is often given in a most baffling order.It's also important to point out that useful examples are almost nonexistent, and this is a major problem considering the level of exercises that Armstrong tries to give his readers. Speaking of the exercises, Armstrong often leaves very important theorems and definitions buried within these as well. And this is not your typical "leave to the exercises" complaint, oh no--he leaves incredibly important definitions and proofs to the reader, such as the existence of the one-point compactification. One may spend an entire class discussing this result, yet Armstrong leaves it to the student.In the end, I would recommend this text to no one. Do not believe those who cite its mathematical "beauty." These people are fools. Get James Munkres's Topology 2nd Edition instead for your first course in Topology. For every terrible thing that I can say about Armstrong, I have a good comment about Munkres. An excellent alternative.