Learning basic topology

>>8179889
Munkres's book.
You don't really need topology for metric spaces though, if you're only interested in analysis you can put that off until like functional analysis I think.
>Online
just use the library genesis.

>>8179896
I'm talking about Rudin's chapter 2, and it looks like that material pops up elsewhere (namely, continuity)

>>8179889
Dover has a book on topology that starts with metric spaces. I think the author is Mendelssohn. It is pretty cheap.

I guess the question that remains is whether a tenuous grasp on the topology, but a solid understanding of metric spaces, would suffice for Rudin? Because to be clear, I'm trying to learn analysis primarily.

>>8179923
It's mainly the exposition, you can read terrence tao's analysis books, Tao is a pretty good expositor. The books cover much less (I think just the first volume of rudin and a bit of the second), but Rudin is pretty bad from a didactical point of view, it's better to just read the rest of the topics somewhere else... (a measure theory, complex analysis, harmonic analysis and functional analysis books).

>>8179935
Luckily there seem to be a lot of online resources. I've actually been going through arose licht in preparation for Rudin, but he's actually not a great expositor either. I wonder if I'm wasting my time with him. At any rate, if I'm not doing too well with the basic topology, should I just move on to sequences? Will I be screwed for continuity?

>>8179889
It's really, really hard to get an intuition for topology. Just memorize the proofs rote, and keep practicing and slowly it will come.

>>8179889
I would also check out the book "Counterexamples in Topology" published by Dover, seeing some bad topology will help you better understand good topology. Although this probably amounts to nothing more than spending more time with the material.

>>8180054
You can learn about continuity in the less general sense of metric space, where it's a bit easier to visualize. Tao's analysis books seem to do that.

>>8180054
I don't think Rudin is a good choice for self study. I would recommend "Real Mathematical Analysis" by Pugh, since it covers mostly the same material as Rudin (in particular it focuses on metric space topology) but it has much better exposition. I haven't read Tao's books but his blog is excellent so I would guess they are good.

Alternatively there are some good video lectures on youtube that helped me a lot with the intuition of topology (they follow Rudin):

https://www.youtube.com/playlist?list=PL0E754696F72137EC

>>8180111
Thanks, I've seen the first few lectures of those series. Unfortunately I made the wrong choice in buying Rosenlicht and (incoming college freshman here -- dependent on parents) am not allowed to buy another one. So Rosenlicht and Rudin it is, unless i find a good pdf.

>>8180059
That's actually sort of encouraging, because that's what I've been doing.

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>>8180111
>Lecture 3: Construction of the Reals

>>8180146
The topology of metric spaces isn't so bad, though! A notion of distance makes things much easier. If you have any specific questions, I can try to relay some intuition to you.

>>8180146
>So Rosenlicht and Rudin it is, unless i find a good pdf.
http://gen.lib.rus.ec/search.php?req=pugh+real+analysis
The second from the bottom is pretty good.