Motivated Reading on Topology?

Question

I am looking for a book on Topology which isn't solely focused on cramming theorems and proofs down the reader's throat: I have already read a significant chunk of Munkres. What I am looking for now is a textbook which can truly cement intuition behind all the basic concepts of the course. If anybody has any recommendations, I would appreciate it. Thank you! (And Happy Holidays!)

(For further context, I will be taking a graduate-level course on Algebraic Topology during Spring. My background in Topology is confined almost entirely to the readings of Munkres over the past week, alongside a brief discussion relating measurable and topological spaces in Real Analysis.)

To provide an example as to what exactly I'm looking for: Paul Halmos' Naive Set Theory. This textbook served a strong role in motivating and therefore teaching the basics to all things Set Theory.

Another example: Folland's Real Analysis: Modern Techniques and Their Applications in comparison with Rudin's Real and Complex Analysis. While I do appreciate the brevity and to-the-point nature of Folland, it can be extraordinarily confusing to a first-time learner: The motivation is lacking, and definitions are sometimes left to the reader to assume understood. Rudin's textbook provides a far more motivated approach to the material, using a direct connection between the study of continuous (and later, Riemann integrable) functions to measurable (and later, Lebesgue integrable) functions. The theory suddenly becomes far more intuitive.

If you know real and complex analysis then you can find, in that subject itself, much of the intuition of general topology: open and closed subsets and their properties; limit points of subsets; interior points of subsets; closures of subsets; interiors of subsets; the definition of continuous functions; ... When reading Munkres, match those topics as they are introduced back with the versions you learned in analysis. — Lee Mosher, Dec 23 '23 at 15:16
But perhaps this answers your question? https://math.stackexchange.com/questions/4411944/textbook-for-first-course-in-point-set-topology?rq=1 — Lee Mosher, Dec 23 '23 at 15:22
Or this? https://math.stackexchange.com/questions/2771955/supplement-book-for-topology/2772097#2772097 — Lee Mosher, Dec 23 '23 at 15:23
For a more geometric oriented overview, Elementary Topology by Dennis Martin Roseman (1999). For a more analysis oriented overview, Introduction to Topology and Modern Analysis by George Finlay Simmons (1963/2003). Given that you'll be taking algebraic topology soon, I recommend Roseman over Simmons. You might also want to look at Algebraic Topology: An Introduction by William Schumacher Massey (1967/1977). — Dave L. Renfro, Dec 23 '23 at 15:32
I was thinking about your question again and it occurred to me that instead of what you asked for, it might be better to focus on the topic of quotient spaces -- read and work through its treatment in several texts. Restricting yourself to quotient space sections of topology texts is a more realistic task for the next few weeks, and this topic will be especially relevant for your algebraic topology course -- see Hatcher Algebraic Topology: I have all the prereqs, so why is this book unreadable for me?. — Dave L. Renfro, Dec 25 '23 at 07:56
Thank you all for your responses! @DaveL.Renfro I will certainly look into the Hatcher Algebraic Topology textbook (I just realized, as I was typing, that's in fact the textbook which'll be used in my course next semester). This should certainly all be very useful. — JAG131, Dec 27 '23 at 15:20
While looking for something else, I came across Notes on Introductory Point-Set Topology (also at archive.org) by Allen Hatcher (author of your upcoming algebraic topology text). Description of the notes -- Hatcher says they form the first part of a topology course he taught in 2005. — Dave L. Renfro, Dec 28 '23 at 18:08

Motivated Reading on Topology?

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