- #1

- 2

- 0

I'm currently taking an undergraduate course in topology. We're using the book

__A Combinatorial Introduction to Topology__, by Michael Henle, and so far I have mixed feelings about it, feelings that my class and professor seem to share.

1. The book doesn't seem to cover enough point set topology for a proper introduction to topology. (Granted, the author seems to be going for a unique approach here.)

2. The book uses less familiar terminology. A point being "near" a set instead of being a "limit point" of a set, and so on.

3. The proofs in the book aren't always very clear.

4. The book treats only topology in the plane, and does not do much with higher dimensional Euclidian spaces, or abstract topological spaces. Some theorems are restricted to the plane, though they hold true in more general situations. (The Bolzano-Weierstrass theorem, for instance.)

5. The exercises are...weird, sometimes. There's the ever-present confusion of whether we're allowed to assume we're in the plane, since that's what the book focuses on. In one problem involving Euler characteristic the n-gon faces of a polytope were just referred to as "cells," causing some confusion.

My professor has resorted to addressing these issues by using some notes on point set topology from a different professor's webpage.

As I understand it, the math department at my school switched from Munkres to Henle fairly recently, the idea being that Munkres was too abstract and didn't include enough pictures for students to develop intuition. Henle has plenty of pictures, and a point in favor of Henle was that it would also introduce students to interesting phenomena in low-dimensional topology --- Mobius strips, Klein bottles, and so forth.

Maybe Munkres is indeed too abstract (I wouldn't know, I haven't read it yet), but I find that professors are often very capable of drawing pictures on a blackboard (mine could probably turn it into a profession with practice), and in fact that's what lecture is for, isn't it? There's also that the course is supposed to introduce the ideas of topology that are useful for analysis, and while I don't know much about algebraic topology it still seems weird that point set topology is so neglected in an introductory topology book.

Has anyone studied/taught/read from Henle's book, and could you tell me your opinions on it? How would you compare it to Armstrong's

__Basic Topology__or Munkres's

__Topology__?