> Great textbook, I learned all the topology I know from it.
The kind of topology this book focuses on is what I learned as "point-set topology". I guess the parent considers topology to not contain algebraic topology, since they go on to say they know more than this book contains.
You could turn this statement around - what if you learned all of the category theory you knew out of this book? Maybe someone can comment.
The start of the book and their take on point-set topology seems reasonable. I saw all of the familiar theorems without any eye-popping machinery being used. I was very happy to see some technically important items in the book (the compact-open topology, and the corresponding topology on Hom).
I would be very interested in a semi-experienced reader's take on Chapter 5. [1]
If you don't already know category theory, is this a reasonable introduction? (Is the on ramp ever smooth?)
I can't vouch for what kind of intro to (point-set) topology the book gives, but I can certainly say that I would prefer this book over MacLane's "Categories for the Working Mathematician" as an introduction to category theory, for what it's worth.
Yes, this textbook is a great introduction to point-set topology. I'm not very familiar with algebraic topology so I can't comment on anything regarding that. I did learn a fair bit of category theory that I didn't know prior, like a formal explanation of deriving the Yoneda Lemma (I read this book before I read CWM). I think it's definitely possible to learn category theory from this book, especially if you already have a strong intuition for Topology.
The kind of topology this book focuses on is what I learned as "point-set topology". I guess the parent considers topology to not contain algebraic topology, since they go on to say they know more than this book contains.
You could turn this statement around - what if you learned all of the category theory you knew out of this book? Maybe someone can comment.
The start of the book and their take on point-set topology seems reasonable. I saw all of the familiar theorems without any eye-popping machinery being used. I was very happy to see some technically important items in the book (the compact-open topology, and the corresponding topology on Hom).
I would be very interested in a semi-experienced reader's take on Chapter 5. [1] If you don't already know category theory, is this a reasonable introduction? (Is the on ramp ever smooth?)
I can't vouch for what kind of intro to (point-set) topology the book gives, but I can certainly say that I would prefer this book over MacLane's "Categories for the Working Mathematician" as an introduction to category theory, for what it's worth.
[1] https://assets.pubpub.org/6d1dqgg9/51597355090422.pdf