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## Main Question or Discussion Point

I've decided that I seriously need to get some topology under my belt, and I've started to tackle the book by Munkres systematically. I only really hope to cover chapters 1-4 and 9 (executive summary for those not famililar with the book: foundational math/ set theory, topological spaces and continuous maps, connectedness and compactness, countability and separation axioms, and a brief intro to algebraic topology- path homotopies, the fundamental group and covering spaces).

I'm trying to work my way through all the corresponding exercises- something I never did enough of as an undergraduate, and I think particularly necessary as I'm studying alone. I'm slightly concerned however that material that looks like it should be easy is taking me a while; the exercises at the end of section 3 have taken me pretty much the whole afternoon. Can anyone suggest a realistic timeframe for me to attempt to master this material? I both hold unrealistic expectations of how long something will take me and dawdle/lose focus/ daydream in equal measure, so I'm really uncertain as to how quickly I should be able to progress through the text.

I'm particularly concerned about the timescale as I'm a theoretical physics PhD student in the UK. This means that a) I only have 3 and a half years to produce a thesis and any study I undertake, so my research should really take priority, and b)my real motivation is not to study topology for its own sake, but to be able to systematically tackle the mathematical literature on differential geometry- in particular, the books by John M Lee on smooth and Riemannian manifolds, and the text by Sharpe with a view to getting a good grasp on gauge theory. (I'd also like to know a hell of a lot more about physics than I presently do ).

As an aside, I do however appreciate that topology can be more directly useful as well, so I'd like to get a reasonable grasp of it as a subject rather than just be able to quote metrisation theorems etc. So any suggestions as to other topics in topology (general or algebraic) that are useful (or even just particularly interesting!) would also be gratefully received.

Thanks in advance.

I'm trying to work my way through all the corresponding exercises- something I never did enough of as an undergraduate, and I think particularly necessary as I'm studying alone. I'm slightly concerned however that material that looks like it should be easy is taking me a while; the exercises at the end of section 3 have taken me pretty much the whole afternoon. Can anyone suggest a realistic timeframe for me to attempt to master this material? I both hold unrealistic expectations of how long something will take me and dawdle/lose focus/ daydream in equal measure, so I'm really uncertain as to how quickly I should be able to progress through the text.

I'm particularly concerned about the timescale as I'm a theoretical physics PhD student in the UK. This means that a) I only have 3 and a half years to produce a thesis and any study I undertake, so my research should really take priority, and b)my real motivation is not to study topology for its own sake, but to be able to systematically tackle the mathematical literature on differential geometry- in particular, the books by John M Lee on smooth and Riemannian manifolds, and the text by Sharpe with a view to getting a good grasp on gauge theory. (I'd also like to know a hell of a lot more about physics than I presently do ).

As an aside, I do however appreciate that topology can be more directly useful as well, so I'd like to get a reasonable grasp of it as a subject rather than just be able to quote metrisation theorems etc. So any suggestions as to other topics in topology (general or algebraic) that are useful (or even just particularly interesting!) would also be gratefully received.

Thanks in advance.